numerical approximation for functionals of reflecting diffusion processes the aim of this paper is to approximate the expectation of a large class of functionals of the solution x xi of a stochastic differential equation with normal reflection in a piecewise smooth domain of rd this also yields a monte carlo method for solving partial differential problems of parabolic type with mixed boundary conditions the approximation is based on a modified euler scheme for the stochastic differential equation the scheme can be driven by a sequence of bounded independently and identically distributed i i d random variables or when the domain is convex by a sequence of gaussian i i d random variables the order of weak convergence for both cases is given in the former case the order of convergence is 1 2 and it is shown to be exact by an example in the last section numerical tests are presented the behavior of the error as a function of the final time t for fixed values of the discretization step and as a function of the discretization step for fixed values of the final

what is the fractional laplacian a comparative review with new results abstract the fractional laplacian in r d which we write as 2 with 0 2 has multiple equivalent characterizations moreover in bounded domains boundary conditions must be incorporated in these characterizations in mathematically distinct ways and there is currently no consensus in the literature as to which definition of the fractional laplacian in bounded domains is most appropriate for a given application the riesz or integral definition for example admits a nonlocal boundary condition where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional laplacian in contrast the spectral definition requires only the standard local boundary condition these differences among others lead us to ask the question what is the fractional laplacian beginning from first principles we compare several commonly used definitions of the fractional laplacian theoretically through their stochastic interpretations as well as their analytical properties then we present quantitative comparisons using a sample of state of the art methods we discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems radial basis function collocation for the riesz fractional laplacian and nonharmonic lifting for the spectral fractional laplacian in our numerical studies we aim to compare different definitions on bounded domains using a collection of benchmark problems we consider the fractional poisson equation with both zero and nonzero boundary conditions where the fractional laplacian is defined according to the riesz definition the spectral definition the directional definition and the horizon based nonlocal definition we verify the accuracy of the numerical methods used in the approximations for each operator and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions through our efforts we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications

infinite dimensional linear programming approach to singularstochastic control we consider a multidimensional singular stochastic control problem with state dependent diffusion matrix and drift vector and control cost depending on the position and direction of displacement of the controlled process the objective is to minimize the total expected discounted cost we write an equivalent infinite dimensional linear programming problem on a subspace of the space conjugate to cal c bbb r n times cal c bbb r n times b where b is the unit sphere in bbb r n we write a dual linear program and prove absence of duality gap the dual program characterizes the optimal cost function as a maximal solution to the variational inequality with gradient constraints

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

a splitting step algorithm for reflected stochastic differential equations in r 1 a new algorithm which is based on the splitting step idea and the penalization method for reflected stochastic differential equation rsde in the upper half space r 1 is presented in this paper after some important estimates about rsdes and penalization odes are obtained the local pathwise error of the suggested algorithm are considered and an estimate of local error in the 2pth moment is proved under the assumptions of lipschitz continuity and linear growth some numerical experiments based on matlab programs are given to support the suggested algorithm

a characterization of 1 perfect additive codes the characterization of perfect single error correcting codes or 1 perfect codes has been an open question for a long time recently rifa has proved that a binary 1 perfect code can be viewed as a distance compatible structure in f sup n and a homomorphism spl theta f sup n spl rarr spl omega where spl omega is a loop a quasi group with identity element in this correspondence we consider 1 perfect codes that are subgroups of f sup n with a distance compatible abelian structure we compute the set of admissible parameters and give a construction for each case we also prove that two such codes are different if they have different parameters the resulting codes are always systematic and we prove their unicity therefore we give a full characterization easy coding and decoding algorithms are also presented

on the additive spl zopf sub 4 linear and non spl zopf sub 4 linear hadamard codes rank and kernel all the possible nonisomorphic additive spl zopf sub 4 linear and non spl zopf sub 4 linear hadamard codes are characterized and the rank and the dimension of the kernel are computed for each one

directional derivatives of oblique reflection maps given an oblique reflection map and functions documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document psi chi in mathcal d lim end document the space of k valued functions that have finite left and right limits at every point the directional derivative documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document nabla chi gamma psi end document of along evaluated at is defined to be the pointwise limit as documentclass aastex usepackage amsbsy usepackage amsfonts u

integration by parts formulae for wiener measures on a path space between two curves this paper is concerned with the integration by parts formulae for the pinned or the standard wiener measures restricted on a space of paths staying between two curves the boundary measures concentrated on the set of paths touching one of the curves once are specified our approach is based on the polygonal approximations in particular to establish the convergence of boundary terms a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons applying the brascamp lieb inequality the stochastic integrals of wiener type are constructed relative to the three dimensional bessel bridge or the brownian meander

lipschitz approximation of the sweeping or moreau process the sweeping process was introduced and solved in the lipschitz case and some other cases but under metric hypotheses by j j moreau 30 31 391 for an intuitive presentation see section 1 then after preliminary papers by h tanaka 47 and c castaing 14 151 m d p monteiro marques 26 27 solved the problem when the multifunction is right lower semi continuous and contains a ball the aim of this paper is to give another proof of the monteiro marques result using an interior lipschitzean approximation of the multifunction our result is slightly less general because we are obliged to assume bilateral lower semi continuity and left closedness of the graph but this is a different approach and it is an opportunity to detail some useful preliminaries for more details see the complete exposure 49

a dirichlet process characterization of a class of reflected diffusions for a class of stochastic differential equations with reflection for which a certain l p continuity condition holds with p 1 it is shown that any weak solution that is a strong markov process can be decomposed into the sum of a local martingale and a continuous adapted process of zero p variation when p 2 this implies that the reflected diffusion is a dirichlet process two examples are provided to motivate such a characterization the first example is a class of multidimensional reflected diffusions in polyhedral conical domains that arise as approximations of certain stochastic networks and the second example is a family of two dimensional reflected diffusions in curved domains in both cases the reflected diffusions are shown to be dirichlet processes but not semimartingales

asymptotically optimal controls for time inhomogeneous networks a framework is introduced for the identification of controls for single class time varying queueing networks that are asymptotically optimal in the so called uniform acceleration regime a related but simpler first order or fluid control problem is first formulated for a class of performance measures that satisfy a certain continuity property it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem examples of performance measures with this property are described and simulations implementing asymptotically optimal policies are presented the use of directional derivatives of the reflection map for solving fluid control problems is also illustrated this work serves to complement a large body of literature on asymptotically optimal controls for time homogeneous networks

propelinear 1 perfect codes from quadratic functions perfect codes obtained by the vasil ev schonheim construction from a linear base code and quadratic switching functions are transitive and moreover propelinear this gives at least exp cn2 propelinear 1 perfect codes of length n over an arbitrary finite field while an upper bound on the number of transitive codes is exp c nlnn 2 vphantom

rate of convergeance of a particle method for the solution of a 1d viscous scalar conservation law in a bounded interval in this paper we give a probabilistic interpretation of a viscous scalar conservation law in a bounded interval thanks to a nonlinear martingale problem the underlying nonlinear stochastic process is reflected at the boundary to take into account the dirichlet conditions after proving uniqueness for the martingale problem we show existence thanks to a propagation of chaos result indeed we exhibit a system of n interacting particles the empirical measure of which converges to the unique solution of the martingale problem as n as a consequence the solution of the viscous conservation law can be approximated thanks to a numerical algorithm based on the simulation of the particle system when this system is discretized in time thanks to the euler lepingle scheme d lepingle math comput simulation 38 1995 119 126 we show that the rate of convergence of the error is in o t 1 n where at denotes the time step finally we give numerical results which confirm this theoretical rate

numerical solutions of linear mixed boundary value problems using stochastic representations the application of ito s formula induces some probabilistic representations of solutions of deterministic linear problems with boundary conditions of dirichlet neumann fourier and mixed types these representations are used to establish some easily implementable algorithms which compute an approximate solution by means of simulation of reflected random walks they do not require selected configurations at the neighbourhood of the domain boundary nor a discretization mesh the associated simulation methods are obtained and applied to problems for each class of boundary conditions numerical experiments with distributed source in two or three dimensional geometries and computational results with estimation of error are reported 1997 by john wiley sons ltd

dynkin games via dirichlet forms and singular control of one dimensional diffusions we consider a zero sum game of optimal stopping in which each of the opponents has the right to stop a one dimensional diffusion process there are two types of costs the first is accumulated continuously at the rate h xt where xt is the current position of the process the second is a cost associated with the stopping of the process it is given by the function f1 x for the first player and the function f2 x for the second player where x is the position of the process when the stopping option is exercised we study the solution of the free boundary problem associated with this game via dirichlet forms on the appropriate functional space integrating the value function of the game we get a solution to another free boundary problem which yields the optimal return function for a singular stochastic control problem

discrete flow networks bottleneck analysis and fluid approximations we conduct bottleneck analysis of a deterministic dynamic discrete flow network the analysis presupposes only the existence of long run averages and is based on a continuous fluid approximation to the network in terms of these averages the results provide functional strong laws of large numbers for stochastic jackson queueing networks since they apply to their sample paths with probability one

an explicit formula for the skorokhod map on 0 a the skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions in this work an explicit formula for the skorokhod map 0 a on 0 a for any a 0 is derived specifically it is shown that on the space d 0 of right continuous functions with left limits taking values in r 0 a a o 0 where a d 0 d 0 is defined by a t t sups 0 t s a infu s t u and 0 d 0 d 0 is the skorokhod map on 0 which is given explicitly by 0 t t sup s 0 t s in addition properties of a are developed and comparison properties of 0 a are established

skew ornstein uhlenbeck processes and their financial applications in this paper we investigate a special class of skew diffusions skew ornstein uhlenbeck abbr ou processes whose scale and speed densities are both piecewise functions the existence and uniqueness of solutions regarding the related stochastic differential equations abbr sdes with local time are established as well as the construction through time changes afterwards we concentrate on three computing issues including the explicit expressions of transition densities the cumulative distributions and laplace transforms of the first hitting times for skew ou processes with the hypothesis on asset dynamics two financial instances in the field of credit risk are illustrated at the end of this paper

on z_ 2 k dual binary codes a new generalization of the gray map is introduced the new generalization phi z2 kn rarr z2 2k 1n is connected with the known generalized gray map phi in the following way if we take two dual linear z2 k codes and construct binary codes from them using the generalizations phi and phi of the gray map then the weight enumerators of the binary codes obtained will satisfy the macwilliams identity the classes of z2 k linear hadamard codes and co z2 k linear extended 1 perfect codes are described where co z2 k linearity means that the code can be obtained from a linear z2 k code with the help of the new generalized gray map

traps for reflected brownian motion consider an open set d r d d 2 and a closed ball b d let e x tb denote the expectation of the hitting time of b for reflected brownian motion in d starting from x d we say that d is a trap domain if supx e x tb a domain d is not a trap domain if and only if the reflecting brownian motion in d is uniformly ergodic we fully characterize the simply connected planar trap domains using a geometric condition and give a number of less complete results for d 2

the reflection map with discontinuities we study the multidimensional reflection map on the spacesd 0 t r k andd 0 8 r k of right continuous r k valued functions on 0 t or 0 8 with left limits endowed with variants of the skorohod 1956 m1 topology the reflection map was used with the continuous mapping theorem by harrison and reiman 1981 and reiman 1984 to establish heavy traffic limit theorems with reflected brownian motion limit processes for vector valued queue length waiting time and workload stochastic processes in single class open queueing networks since brownian motion and reflected brownian motion have continuous sample paths the topology of uniform convergence over bounded intervals could be used for those results variants of them1 topologies are needed to obtain alternative discontinuous limits approached gradually by the converging processes as occurs in stochastic fluid networks with bursty exogenous input processes e g with on off sources having heavy tailed on periods or off periods having infinite variance we show that the reflection map is continuous at limits without simultaneous jumps of opposite sign in the coordinate functions provided that the productm1 topology is used as a consequence the reflection map is continuous with the productm1 topology at all functions that have discontinuities in only one coordinate at a time that continuity property also holds for more general reflection maps and is sufficient to support limit theorems for stochastic processes in most applications we apply the continuity of the reflection map to obtain limits for buffer content stochastic processes in stochastic fluid networks

probabilistic approach for nonlinear partial differential equations and stochastic partial differential equations with neumann boundary conditions abstract in this study we consider nonlinear partial differential equations pdes and stochastic pdes spdes with neumann boundary conditions on domains that satisfy the lions sznitmann saisho conditions using the convergence result based on the penalization approximation for stochastic differential equations with normal reflections on nonsmooth and nonconvex domains we establish the existence and comparison principle for the viscosity solutions of nonlinear pdes with the neumann conditions associated with the optimal control problem we also obtain for nonlinear spdes and backward spdes with neumann condition the representations of the stochastic viscosity solutions

translation invariant propelinear codes a class of binary group codes is investigated these codes are the propelinear codes defined over the hamming metric space f sup m f 0 1 with a group structure generally they are neither abelian nor translation invariant codes but they have good algebraic and combinatorial properties linear codes and z sub 4 linear codes can be seen as a subclass of propelinear codes it is shown here that the subclass of translation invariant propelinear codes is of type z sub 2 sup k1 spl oplus z sub 4 sup k2 spl oplus q sub 8 k3 where q sub 8 is the non abelian quaternion group of eight elements exactly every translation invariant propelinear code of length n can be seen as a subgroup of z sub 2 sup k1 spl oplus z sub 4 sup k2 spl oplus q sub 8 sup k3 with k sub 1 2k sub 2 4k sub 3 n for k sub 2 k sub 3 0 we obtain linear binary codes and for k sub 1 k sub 3 0 we obtain z sub 4 linear codes the class of additive propelinear codes the abelian subclass of the translation invariant propelinear codes is studied and a family of nonlinear binary perfect codes with a very simply construction and a very simply decoding algorithm is presented

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

the skorohod oblique reflection problem in domains with corners and application to stochastic differential equations the skorohod oblique reflection problem for d w d a general domain in d x x d a convex cone of directions of reflection w a function ind d is considered it is first proved under a condition on d corresponding to x not being simultaneously too large and too much skewed with respect to d that given a sequence wn of functions converging in the skorohod topology tow any sequence xn n of solutions to the skorohod problem for d wn is relatively compact and any of its limit points is a solution to the skorohod problem for d w next it is shown that if d satisfies the uniform exterior sphere condition and another requirement then solutions to the skorohod problem for d w exist for everyw d d with small enough jump size the requirement is met in the case when d is piecewisecb1 is generated by continuous vector fields on the faces ofd and x makes and angle in a suitable sense of less than 2 with the cone of inward normals atd for everyx d existence of obliquely reflecting brownian motion and of weak solutions to stochastic differential equations with oblique reflection boundary conditions is derived

fluctuations for a φ interface model with repulsion from a wall we consider a interface model on a one dimensional lattice with repulsion from a hard wall we suppose that the repulsion is of the form c 1 where c 0 and denotes the height of the interface from the wall we prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a spde with singular drift if c 0 the system becomes the funaki olla interface model with reflection at the wall whose equilibrium fluctuations converge to the solution of a spde with reflection we give a new proof of this result using the characterization of such solution as the diffusion generated by an infinite dimensional dirichlet form obtained in a previous paper our method is based on a study of integration by parts formulae w r t the equilibrium measure of the interface model and allows to avoid the proof of the so called boltzmann gibbs principle we also obtain convergence of finite dimensional distributions of non equilibrium fluctuations around the stationary hydrodynamic limit 0

a system of infinitely many mutually reflecting brownian balls in ℝd an infinite system of skorohod type equations is studied the unique solution of the system is obtained from a finite case by passing to the limit it is a diffusion process describing a system of infinitely many brownian hard balls and has a gibbs state associated with the hard core pair potential as a reversible measure

a stochastic differential game in the orthrant we study a zero sum stochastic differential game in the nonnegative orthrant the state of the system is governed by controlled reflecting diffusions in the nonnegative orthrant we consider discounted and average payoff evaluation criteria we prove the existence of values and optimal strategies for both payoff criteria

asymptotically optimal admission control of a queue with impatient customers we consider a gi gi 1 queue with impatient customers in heavy traffic we use the solution of an approximating singular diffusion control problem to construct an admission control policy for the queue the approximating control problem does not admit a so called pathwise solution hence the resulting admission control policy depends on second moment data we prove asymptotic optimality of the constructed policy using weak convergence methods rh

on binary 1 perfect additive codes some structural properties the rank and kernel of 1 perfect additive codes is determined additive codes could be seen as translation invariant propelinear codes and in this correspondence a characterization of propelinear codes as codes having a regular subgroup of the full group of isometrics of the code is established a characterization of the automorphism group of a 1 perfect additive code is given and also the cardinality of this group is computed finally an efficiently computable characterization of the steiner triple systems associated with a 1 perfect binary additive code is also established

system of interacting particles and nonlinear diffusion reflecting in a domain with sticky boundary we study a system of particles and the nonlinear mckean vlasov diffusion that is its limit for weak interactions in statistical mechanics reflecting in a domain with sticky boundary the interaction takes place in particular in the sojourn condition we show existence and uniqueness for the nonlinear martingale problem by a contraction argument on time change then we construct the system of particles by a limiting procedure and show propagation of chaos towards the nonlinear diffusion

spaces snu diametral dimension and property omega bar abstract we provide new developments to extend the formula of the diametral dimension of locally p convex spaces s aubry and bastin 2010 to some locally pseudoconvex ones we also use our method to prove that the spaces s verify the property of vogt and wagner in case they are locally p convex and for some cases of local pseudoconvexity

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

an irreversible investment problem with maintenance expenditure on a finite horizon free boundary analysis abstract this paper concerns a continuous time finite horizon optimal irreversible investment problem with maintenance expenditure of a firm under uncertainty we assume that the firm can make irreversible investments to expand its production capacity and spend maintenance expenditure to achieve better performance of the productivity the objective of the firm is to construct optimal investment and maintenance policies to maximize its expected total profit over a finite horizon mathematically it is a singular stochastic control problem whose value function satisfies a parabolic variational inequality with gradient constraint the problem gives rise to two free boundaries which stand for the optimal investment and maintenance strategies respectively we investigate behaviors of free boundaries study regularities of the value function and give optimal investment and maintenance policies as we know this is a first integral result for an investment maintenance problem with a finite time horizon due to use of partial differential equation pde technique

heavy traffic limits for the g h2 n m queue we establish heavy traffic stochastic process limits for queue length waiting time and overflow stochastic processes in a class ofg gi n m queueing models withn servers andm extra waiting spaces we let the arrival process be general only requiring that it satisfy a functional central limit theorem to capture the impact of the service time distribution beyond its mean within a markovian framework we consider a special class of service time distributions denoted byh2 which are mixtures of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1 p these service time distributions exhibit relatively high variability having squared coefficients of variation greater than or equal to one as in halfin and whitt 1981 heavy traffic limits for queues with many exponential servers oper res 29 567 588 puhalskii and reiman 2000 the multiclassgi ph n queue in the halfin whitt regime adv appl probab 32 564 595 and garnett mandelbaum and reiman 2002 designing a call center with impatient customers manufacturing service oper management 4 208 227 we consider a sequence of queueing models indexed by the number of servers n and letn tend to infinity along with the traffic intensities nso that v n 1 n for 8 8 to treat finite waiting rooms we letm n v n for 0 8 with the specialh2 service time distribution the limit processes are one dimensional markov processes behaving like diffusion processes with different drift and diffusion functions in two different regions above and below zero we also establish a limit for theg m n m m model having exponential customer abandonments

intrinsic gaussian processes on complex constrained domains we propose a class of intrinsic gaussian processes gps for interpolation regression and classification on manifolds with a primary focus on complex constrained domains or irregularly shaped spaces arising as subsets or submanifolds of r r2 r3 and beyond for example intrinsic gps can accommodate spatial domains arising as complex subsets of euclidean space intrinsic gps respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces the key novelty of the approach proposed is to utilize the relationship between heat kernels and the transition density of brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels this enables intrinsic gps to be practically applied in great generality whereas existing approaches for smoothing on constrained domains are limited to simple special cases the broad utilities of the intrinsic gp approach are illustrated through simulation studies and data examples

reaction diffusion on metric graphs from 3d to 1d abstract we provide stochastic foundations for the analysis of a class of reaction diffusion systems using as an example the known temporal analysis of products tap experiments showing how to effectively obtain explicit solutions to the associated equations by approximating the 3 dimensional domain of diffusion u the reactor by 1 dimensional network models in a typical tap experiment a pulse of reactant gas of species a is injected into u which is filled with chemically inert material permeable to gas diffusion particles of catalyst are placed amid this inert medium forming active sites where the reaction a b may occur on part of the boundary of u designated as the exit a mixture of a and b can escape we study the problem of determining the molar fraction of product gas in the mixture after u is fully evacuated this fraction is identified with the reaction probability that is the probability of a single diffusing molecule reacting before leaving u specifically we are interested in how this probability depends on the reaction rate constant k after giving a stochastic formulation of the problem and the boundary value problem whose solution is this probability we study a class of domains called fat graphs comprising a network of thin tubes with active sites at junctures the main result of the paper is that in the limit as the thin tubes approach curves in 3 dimensional space reaction probability converges to functions of the point of gas injection that can be computed explicitly in terms of a rescaled parameter k by this 3d to 1d reduction the simpler processes on metric graphs can be used as model systems for more realistic 3 dimensional configurations this is illustrated with analytic and numerical examples one example in particular illustrates an important application of our method finding the catalyst configuration that maximizes reaction probability at a given reaction rate constant

on reflecting boundary problem for optimal control this paper deals with mayer s problem for controlled systems with reflection on the boundary of a closed subset k the main result is the characterization of the possibly discontinuous value function in terms of a unique solution in a suitable sense to a partial differential equation of hamilton jacobi bellman type

the skorohod oblique reflection problem in time dependent domains the deterministic skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection in the form studied here the multidimensional skorohod problem w

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

lifschitz tail on hyperbolic space neumann conditions on considere un espace hyperbolique h de dimension n et l operateur laplacien hyperbolique h etant donne une distribution aleatoire de points a l aide d un processus ponctuel de poisson tel que chaque point se situe dans une boule hyperbolique de rayons on etudie la question suivante si est un petit nombre reel combien y a t il de valeurs propres inferieures a pour l operateur 1 2 h dans une boule b de centre o avec des conditions de neumann sur la frontiere et avec des conditions aux limites de dirichlet sur les boules aleatoires formant des intersections avec b si le rayon de b est suffisamment grand

algebraic lattice constellations bounds on performance in this work we give a bound on performance of any full diversity lattice constellation constructed from algebraic number fields we show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain furthermore we discuss constructions minimum product distance and bounds for full diversity complex rotated z i sup n lattices for any dimension n which avoid the need of component interleaving

advanced topology on the multiscale sequence spaces s nu abstract we pursue the study of the multiscale spaces s introduced by jaffard in the context of multifractal analysis we give the necessary and sufficient condition for s to be locally p convex and exhibit a sequence of p norms that defines its natural topology the strong topological dual of s is identified to another sequence space depending on endowed with an inductive limit topology as a particular case we describe the dual of a countable intersection of besov spaces

topological properties of the sequence spaces s nu abstract we define sequence spaces based on the distributions of the wavelet coefficients in the spirit of s jaffard beyond besov spaces part i distributions of wavelet coefficients j fourier anal appl 10 2004 221 246 we study their topology and especially show that they can be endowed with a unique complete metric for which compact sets can be explicitly described and we study properties of this metric we also give relationships with besov spaces

a differential game for a multiclass queueing model in the moderate deviation heavy traffic regime we study a differential game that governs the moderate deviation heavy traffic asymptotics of a multiclass single server queueing control problem with a risk sensitive cost we consider a cost set on a finite but sufficiently large time horizon and show that this formulation leads to stationary feedback policies for the game several aspects of the game are explored including its characterization via a one dimensional free boundary problem the semi explicit solution of an optimal strategy and the specification of a saddle point we emphasize the analogy to the well known harrison taksar free boundary problem which plays a similar role in the diffusion scale heavy traffic literature

continuous dependence results for non linear neumann type boundary value problems abstract we obtain estimates on the continuous dependence on the coefficient for second order non linear degenerate neumann type boundary value problems our results extend previous work of cockburn et al jakobsen and karlsen and gripenberg to problems with more general boundary conditions and domains a new feature here is that we account for the dependence on the boundary conditions as one application of our continuous dependence results we derive for the first time the rate of convergence for the vanishing viscosity method for such problems we also derive new explicit continuous dependence on the coefficients results for problems involving bellman isaacs equations and certain quasilinear equation

on the oblique derivative problem for diffusion processes and diffusion equations with holder continuous coefficients on a c2 domain in a euclidean space we consider the oblique derivative problem for a diffusion equation and assume the coefficients of the diffusion and boundary operators are holder continuous we then prove the uniqueness of diffusion processes and fundamental solutions corresponding to the problem for the purpose obtaining a stochastic representation of some so lutions to the problem plays a key role in our situation a difficulty arises from the absence of a fundamental solution with c2 smoothness up to the boundary it is overcome by showing some stability of a fundamental solution and a dif fusion process respectively under approximation of the domain in particular the stability of the fundamental solution is verified through construction it is done by applying the parametrix method twice to a parametrix with explicit expression

approximating the gi gi 1 gi queue with a nonlinear drift diffusion hazard rate scaling in heavy traffic we study a single server queue operating under the first in first out fifo service discipline in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time under some mild conditions on the abandonment distribution we identify a limiting heavy traffic regime in which the resulting diffusion approximation for both the offered waiting time process the process that tracks the amount of time an infinitely patient arriving customer would wait for service and the queue length process contain the entire abandonment distribution to use a continuous mapping approach to establish our weak convergence results we additionally develop existence uniqueness and continuity results for nonlinear generalized regulator mappings that are of independent interest we further perform a simulation study to evaluate the quality of the proposed approximations for the steady state mean queue length and the steady state probability of abandonment suggested by the limiting diffusion process

the submartingale problem for a class of degenerate elliptic operators we consider the degenerate elliptic operator acting on c 2 b functions on 0 d mathcal l f x sum i 1 d a i x x i alpha i frac partial 2 f partial x i 2 x sum i 1 d b i x frac partial f partial x i x where the ai are continuous functions that are bounded above and below by positive constants the bi are bounded and measurable and the alpha i in 0 1 we impose neumann boundary conditions on the boundary of 0 d there will not be uniqueness for the submartingale problem corresponding to mathcal l if we consider however only those solutions to the submartingale problem for which the process spends 0 time on the boundary then existence and uniqueness for the submartingale problem for mathcal l holds within this class our result is equivalent to establishing weak uniqueness for the system of stochastic differential equations rm d x t i sqrt 2a i x t x t i alpha i 2 rm d w i t b i x t rm d t rm d l t x i quad x i t geq 0 where w t i are independent brownian motions and l x i t is a local time at 0 for xi

reflected brownian motion in a cone semimartingale property in this paper the object of study is reflected brownian motion in a cone ind dimensions d 3 with nonconstant oblique reflection on each radial line emanating from the vertex of the cone the basic question considered here is when is this process a semimartingale conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by kwon which is resolved in terms of a real parameter depending on the cone and the direction of reflection it is shown that starting from any point of the cone the process is a semimartingale if 1 0 and not a semimartingale if 2

optimal beamforming for video streaming in multiantenna interference networks via diffusion limit in this paper we consider queue aware beamforming control for video streaming applications in multiantenna interference network using heavy traffic approach we derive the diffusion limit for the discrete time queuing system and obtain an ergodic excess beamforming control problem for the diffusion limit system the ergodic control problem is to minimize the average power costs of the access points subject to the constraints on the playback interruption costs and buffer overflow costs of the mobile users to deal with the queue coupling challenge we utilize the weak interference coupling property in the network using the theories of calculus and perturbation techniques we derive a closed form approximate priority function of the optimality equation and the associated error bound based on this approximation we propose a low complexity queue aware beamforming control algorithm which is asymptotically optimal for sufficiently small cross channel path gain finally the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved

the submartingal problem for brownian motion in a cone with non constant oblique reflection this work is concerned with the existence and uniqueness of a strong markov process that has continuous sample paths and the following additional properties 1 the state space is a cone ind dimensions d 3 and the process behaves in the interior of the cone like ordinary brownian motion 2 the process reflects instantaneously at the boundary of the cone the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial line emanating from the vertex 3 the amount of time that the process spends at the vertex of the cone is zero i e the set of times for which the process is at the vertex has zero lebesgue measure

brownian motion in a wedge with variable skew reflection does planar brownian motion confined to a wedge by skew reflection on the sides approach the vertex of the wedge this question has been answered by varadhan and williams in the case where the direction of reflection is constant on each of the sides but here we address the question when the direction reflected is allowed to vary a necessary condition and a sufficient condition are obtained for the vertex to be reached the conditions are of a geometric nature and the gap between them is quite small

set estimation from reflected brownian motion we study the problem of estimating a compact set s rd from a trajectory of a reflected brownian motion in s with reflections on the boundary of s this problem has relevant applications in ecology in estimating the home range of an animal based on tracking data

the problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures abstract we obtain a linear programming characterization for the minimum cost associated with finite dimensional reflected optimal control problems in order to describe the value functions we employ an infinite dimensional dual formulation instead of using the characterization via hamilton jacobi partial differential equations in this paper we consider control problems with both infinite and finite horizons the reflection is given by the normal cone to a proximal retract set

on neumann eigenfunctions in lip domains atar s research partially supported by the fund for the promotion of research at the technion burdzy gratefull acknowledges the hospitality and financial support of technion israel and institut mittag leffler sweden this research was partially supported by nsf grant dms 0071486 and isf grant 12 98

the rank and kernel of extended 1 perfect spl zopf sub 4 linear and additive non spl zopf sub 4 linear codes a binary extended 1 perfect code of length n 1 2 sup t is additive if it is a subgroup of spl zopf sub 2 sup spl alpha spl times spl zopf sub 4 sup spl beta the punctured code by deleting a spl zopf sub 2 coordinate if there is one gives a perfect additive code 1 perfect additive codes were completely characterized and by using that characterization we compute the possible parameters spl alpha spl beta rank and dimension of the kernel for extended 1 perfect additive codes a very special case is that of extended 1 perfect spl zopf sub 4 linear codes

a multidimensional process involving local time on presente une approche probabiliste a un probleme pose par mckean 1967 pour la construction d un systeme de n particules sur r avec un generateur formel

optimal reflection of diffusions and barrier options pricing under constraints we introduce a new class of control problems in which the gain depends on the solution of a stochastic differential equation sde reflected at the boundary of a bounded domain along directions which are controlled by a bounded variation process we provide a pde characterization of the associated value function this study is motivated by applications in mathematical finance where such equations are related to the pricing of barrier options under portfolio constraints

regularity of the value function for a two dimensional singular stochastic control problem it is desired to control a two dimensional brownian motion by adding a possibly singularly continuous process to it so as to minimize an expected infinite horizon discounted running cost the hamilton jacobi bellman characterization of the value function v is a variational inequality which has a unique twice continuously differentiable solution the optimal control process is constructed by solving the skorokhod problem of reflecting the two dimensional brownian motion along a free boundary in the nabla v direction

strong feller properties for distorted brownian motion with reflecting boundary condition and an application to continuous n particle systems with singular interactions abstract assuming that r n n 2 is an open relatively compact set with boundary of lebesgue measure zero we prove strong feller properties for a class of distorted brownian motions in with reflecting boundary condition dirichlet form techniques give the existence of a weak solution to the corresponding stochastic differential equation for quasi all starting points in the sense of the associated martingale problem combining this result with the strong feller properties we can construct a weak solution for specified starting points if has c 2 boundary the construction works for all starting points where the drift term is not singular even on the boundary but also for a certain class of sets with less smooth boundary our approach works for all points in where the drift term is not singular and at least some points from our techniques allow very singular drift terms this enables us to construct continuous n particle gradient stochastic dynamics in cuboids r d d n with reflecting boundary condition and singular interactions for d n 2 we can start the stochastic dynamics in all initial configurations having at most one particle in provided is locally smooth there

generalized bsdes and nonlinear neumann boundary value problems we study a new class of backward stochastic differential equations which involves the integral with respect to a continuous increasing process this allows us to give a probabilistic formula for solutions of semilinear partial differential equations with neumann boundary condition where the boundary condition itself is nonlinear we consider both parabolic and elliptic equations