error probability bounds and approximations for ds spread spectrum communication systems with mutiple tone or multiple access interference upper and lower bounds on the average probability of error of direct sequence ds spread spectrum communication systems operating in the presence of either multiple tone or multiple access interference are presented the bounds are quite tight and can be used without the restriction that the peak level of the interference be less than the desired signal level a simple method for evaluating approximations to the bounds for multiple access systems in which the peak interference does indeed exceed the desired signal level is presented as well the tightness of both the bounds and the approximations are illustrated with numerical results

an extension of kesten s criterion for amenability to topological markov chains abstract the main results of this note extend a theorem of kesten for symmetric random walks on discrete groups to group extensions of topological markov chains in contrast to the result in probability theory there is a notable asymmetry in the assumptions on the base that is it turns out that under very mild assumptions on the continuity and symmetry of the associated potential amenability of the group implies that the gurevic pressures of the extension and the base coincide whereas the converse holds true if the potential is holder continuous and the topological markov chain has big images and preimages finally an application to periodic hyperbolic manifolds is given

reflected mean field backward stochastic differential equations approximation and associated nonlinear pdes abstract mathematical mean field approaches have been used in many fields not only in physics and chemistry but also recently in finance economics and game theory in this paper we will study a new special mean field problem in a purely probabilistic method to characterize its limit which is the solution of mean field backward stochastic differential equations bsdes with reflections on the other hand we will prove that this type of reflected mean field bsdes can also be obtained as the limit equation of the mean field bsdes by penalization method finally we give the probabilistic interpretation of the nonlinear and nonlocal partial differential equations with the obstacles by the solutions of reflected mean field bsdes

multidimensional viscosity solution theory of semi linear partial differential equations abstract in this paper we concern the multidimensional viscosity solution theory of a kind of semi linear partial differential equations pdes a new definition of viscosity solution for this multidimensional semi linear pdes is given furthermore we establish the existence and uniqueness results for the viscosity solution of this semi linear pdes via the comparison theorem of the related backward stochastic differential equations bsdes and a smooth approximation techniques

reflected solutions of backward sde s and related obstacle problems for pde s we study reflected solutions of one dimensional backward stochastic differential equations the reflection keeps the solution above a given stochastic process we prove uniqueness and existence both by a fixed point argument and by approximation via penalization we show that when the coefficient has a special form then the solution of our problem is the value function of a mixed optimal stopping optimal stochastic control problem we finally show that when put in a markovian framework the solution of our reflected bsde provides a probabilistic formula for the unique viscosity solution of an obstacle problem for a parabolic partial differential equation

error probability for direct sequence spread spectrum multiple access communications part i upper and lower bounds upper and lower bounds on the average probability of error are obtained for direct sequence spread spectrum multipleaccess communications systems with additive white gaussian noise channels the bounds which are developed from convexity properties of the error probability function are valid for systems in which the maximum multiple access interference does not exceed the desired signal and the signature sequence period is equal to the duration of the data pulse the tightness of the bounds is examined for systems with a small number of simultaneously active transmitters this is accomplished by comparisons of the upper and lower bounds for several values of the system parameters the bounds are also compared with an approximation based on the signal to noise ratio and with the chernoff upper bound

a sufficient stochastic maximum principle for a kind of recursive optimal control problem with obstacle constraint abstract in this paper we study a kind of recursive optimal control problem whose utility functional is described by the solution of a reflected backward stochastic differential equation bsde we obtain a sufficient stochastic maximum principle of optimal controls moreover a mixed optimal control problem is considered to illustrate the application of our theoretical result and the optimal control and stopping strategy are given

real analyticity of hausdorff dimension for higher dimensional hyperbolic graph directed markov systems in this paper we prove that the hausdorff dimension function of the limit sets of strongly regular hyperbolic conformal graph directed markov systems living in higher dimensional euclidean spaces mathbb r d d ge 3 and with an underlying finitely irreducible incidence matrix is real analytic

on the critical exponent of infinitely generated veech groups we prove the existence of veech groups having a critical exponent strictly greater than any elementary fuchsian group i e frac 1 2 but strictly smaller than any lattice i e 1 more precisely every affine covering y of a primitive l shaped veech surface x ramified over the singularity and a non periodic connection point p in x has such a veech group mathrm sl y hubert and schmidt duke math j 123 49 69 2004 showed that these veech groups are infinitely generated and of the first kind we use a result of roblin and tapie monogr enseign math 43 61 92 2013 which connects the critical exponent of mathrm sl y with the cheeger constant of the schreier graph of mathrm sl x mathrm stab mathrm sl x p the main task is to show that the cheeger constant is strictly positive i e the graph is non amenable in this context we introduce a measure of the complexity of connection points that helps to simplify the graph to a forest for which non amenability can be seen easily

dynamic programming principle for one kind of stochastic recursive optimal control problem and hamilton jacobi bellman equation in this paper we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation we give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding hamilton jacobi bellman equation

backward doubly stochastic differential equations with weak assumptions on the coefficients in this paper we deal with one dimensional backward doubly stochastic differential equations bdsdes we obtain existence theorems and comparison theorems for solutions of bdsdes with weak assumptions on the coefficients

cogrowth and amenability of discrete groups abstract let g be a group and g1 gt a set of generators there are approximately 2t 1 n reduced words in g1 gt of length n let gg n be the number of those which represent 1g we show that lim n gg n 1 n exists clearly 1 2t 1 log log 2t 1 is the cogrowth 0 1 in fact 0 1 2 1 the entropic dimension of g is shown to be 1 it is then proved that d g 1 if and only if g is free on g1 gt and d g 0 if and only if g is amenable

stochastic verification theorem of forward backward controlled systems for viscosity solutions abstract in this paper we investigate the controlled systems described by forward backward stochastic differential equations with the control contained in drift diffusion and generator of bsdes a new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions it is worth pointing out that this theorem has wider applicability than the restrictive classical verification theorems as a relevant problem the optimal stochastic feedback controls for forward backward systems are discussed as well

on the bottom of spectra under coverings for a riemannian covering m 1 rightarrow m 0 of connected riemannian manifolds with respective fundamental groups gamma 1 subseteq gamma 0 we show that the bottoms of the spectra of m 0 and m 1 coincide if the right action of gamma 0 on gamma 1 backslash gamma 0 is amenable

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

stochastic differential games and viscosity solutions of hamilton jacobi bellman isaacs equations in this paper we study zero sum two player stochastic differential games with the help of the theory of backward stochastic differential equations bsdes more precisely we generalize the results of the pioneering work of fleming and souganidis indiana univ math j 38 1989 pp 293 314 by considering cost functionals defined by controlled bsdes and by allowing the admissible control processes to depend on events occurring before the beginning of the game this extension of the class of admissible control processes has the consequence that the cost functionals become random variables however by making use of a girsanov transformation argument which is new in this context we prove that the upper and the lower value functions of the game remain deterministic apart from the fact that this extension of the class of admissible control processes is quite natural and reflects the behavior of the players who always use the maximum of available information its combination with bsde methods in particular that of the notion of stochastic backward semigroups introduced by peng bsde and stochastic optimizations in topics in stochastic analysis science press beijing 1997 allows us then to prove a dynamic programming principle for both the upper and the lower value functions of the game in a straightforward way the upper and the lower value functions are then shown to be the unique viscosity solutions of the upper and the lower hamilton jacobi bellman isaacs equations respectively for this peng s bsde method is extended from the framework of stochastic control theory into that of stochastic differential games

the maximum principle for stochastic differential systems with general cost functional abstract in this paper under the framework of frechet derivatives we study a stochastic optimal control problem driven by a stochastic differential equation with general cost functional by constructing a series of first order and second order adjoint equations we establish the stochastic maximum principle and get the related hamilton systems

amenability critical exponents of subgroups and growth of closed geodesics let gamma be a non elementary convex co compact group of isometries of a pinched hadamard manifold x we show that a normal subgroup gamma 0 has critical exponent equal to the critical exponent of gamma if and only if gamma gamma 0 is amenable we prove a similar result for the exponential growth rate of closed geodesics on x gamma these statements are analogues of classical results of kesten for random walks on groups and brooks for the spectrum of the laplacian on covers of riemannian manifolds

computationally efficient bounds for the performance of direct sequence spread spectrum multiple access communications systems in jamming environments an approach for calculating upper and lower bounds for the probability of error for asynchronous multiple access spread spectrum communication systems using deterministic codes is presented the techniques is then generalized to include multiple tone jamming the approach utilizes the cumulative distribution function of individual interference terms the computational complexity of the technique is calculated to the polynomial like results showing the multiple access performance of gold codes of lengths 31 and 127 in the presence of jamming are shown the fact that this computational technique gives upper and lower bounds is rigorously proved using the riemann stieltjes integral

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

optimum multiuser asymptotic efficiency the degradation in bit error rate due to the presence of multiple access interference in a white gaussian channel can be measured by the multiuser asymptotic efficiency defined as the ratio between the snr required to achieve the same uncoded bit error rate in the absence of interfering users and the actual snr in this paper the asymptotic efficiency of the optimum multiuser demodulator a bank of matched filters followed by a viterbi algorithm is investigated and compared to that of the conventional single user matched filter receiver the computation of the optimum asymptotic efficiency of any given user is equivalent to the minimization of the euclidean distance between any pair of multiuser signals which differ in at least one of the symbols of that user it is shown that the optimum multiuser efficiency of asynchronous systems is nonzero with probability 1 and therefore the optimum demodulator does not become multiple access limited in contrast to the single user receiver a class of signal constellations with moderate cross correlation requirements is shown to achieve unit optimum multiuser efficiencies and hence to be equivalent to orthogonal signal sets from the viewpoint of performance of the optimum multiuser detector

the effect of multiple tone interfering signals on a direct sequence spread spectrum communication system the chernoff bound is used to upper bound the average probability of error of a direct sequence spread spectrum communication system under the conditions of multiple tone interference a special case is analyzed using a gaussian approximation to the interference and this latter result is compared to that predicted by the chernoff bound the limitations of the gaussian approximation are then carefully explained

stochastic recursive optimal control problem of reflected stochastic differential systems in this paper we study one kind of stochastic recursive optimal control problem in which the control system is stochastic differential equations reflected in a domain and the cost functional is de

singular optimal controls of stochastic recursive systems and hamilton jacobi bellman inequality abstract in this paper we study the optimal singular controls for stochastic recursive systems in which the control has two components the regular control and the singular control under certain assumptions we establish the dynamic programming principle for this kind of optimal singular controls problem and prove that the value function is a unique viscosity solution of the corresponding hamilton jacobi bellman inequality in a given class of bounded and continuous functions at last an example is given for illustration

sobolev weak solutions of the hamilton jacobi bellman equations this paper is concerned with the sobolev weak solutions of the hamilton jacobi bellman hjb equations these equations are derived from the dynamic programming principle in the study of stochastic optimal control problems adopting the doob meyer decomposition theorem as one of the main tools we prove that the optimal value function is the unique sobolev weak solution of the corresponding hjb equation in the recursive optimal control problem the cost function is described by the solution of a backward stochastic differential equation bsde this problem has a practical background in economics and finance we prove that the value function is the unique sobolev weak solution of the related hjb equation by virtue of the nonlinear doob meyer decomposition theorem introduced in the study of bsdes

a pontryagin s maximum principle for non zero sum differential games of bsdes with applications this technical note is concerned with a maximum principle for a new class of non zero sum stochastic differential games the most distinguishing feature compared with the existing literature is that the game systems are described by backward stochastic differential equations bsdes this kind of games are motivated by some interesting phenomena arising from financial markets and can be used to characterize the players with different levels of utilities we establish a necessary condition and a sufficient condition in the form of maximum principle for open loop equilibrium point of the foregoing games respectively to explain the theoretical results we use them to study a financial problem

necessary condition for near optimal control of linear forward backward stochastic differential equations this paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations where both the drift and diffusion terms are allowed to depend on controls and the control domain is not assumed to be convex in the previous work theorem 3 1 of the second and third authors some problem of near optimal control with the control dependent diffusion is addressed and our current paper can be viewed as some direct response to it the necessary condition of the near optimality is established within the framework of optimality variational principle developed by yong and obtained by the convergence technique to treat the optimal control of fbsdes in unbounded control domains by wu some new estimates are given here to handle the near optimality in addition an illustrating example is discussed as well

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

maximum principle for forward backward sdes with a general cost functional abstractin this study we consider a stochastic optimal control problem whose state variables are described by the system of forward and backward stochastic differential equations with a general cost functional which relies on the global terminal condition in the framework of frechet derivatives we derive the corresponding maximum principle via constructing a series of adjoint equations which need to be solved step by step

critical exponents of normal subgroups the spectrum of group extended transfer operators and kazhdan distance abstract for a pinched hadamard manifold x and a discrete group of isometries of x the critical exponent is the exponential growth rate of the orbit of a point in x under the action of we show that the critical exponent for any family n of normal subgroups of 0 has the same coarse behaviour as the kazhdan distances for the right regular representations of the quotients 0 the key tool is to analyse the spectrum of transfer operators associated to subshifts of finite type for which we obtain a result of independent interest

coded error probability for ds spread spectrum systems with periodic pulsed multiple tone interference the coded error probability for direct sequence ds bpsk or qpsk spread spectrum systems used with or without interleaving and operating in the presence of pulsed multiple tone interference is investigated we consider the worst case channel error probability under conditions of pulsed multiple tone jamming for the various systems and present coded error probability as a function of interleaving delay for n k block codes with hard decision decoding it is shown that when the maximum level of continuous multiple tone interference does not exceed the level of the desired signal the duty cycle of the corresponding pulsed interference which yields the worst case error probability is usually small and that the smaller the duty factor of the jamming the more considerable is the performance improvement due to the use of interleaving in conjunction with the coding

bounds for eigenfunctions of the laplacian on noncompact riemannian manifolds we deal with eigenvalue problems for the laplacian on noncompact riemannian manifolds m of finite volume sharp conditions ensuring l q m and l infinity m bounds for eigenfunctions are exhibited

regularity properties for general hjb equations a backward stochastic differential equation method in this work we investigate regularity properties of a large class of hamilton jacobi bellman hjb equations with or without obstacles which can be stochastically interpreted in the form of a stochastic control system in which nonlinear cost functional is defined with the help of a backward stochastic differential equation bsde or a reflected bsde more precisely we prove that first the unique viscosity solution v t x of an hjb equation over the time interval 0 t with or without an obstacle and with terminal condition at time t is jointly lipschitz in t x f ort running any compact subinterval of 0 t second for the case that v solves an hjb equation without an obstacle or with an upper obstacle it is shown under appropriate assumptions that v t x i s jointly semiconcave in t x these results extend earlier ones by buckdahn cannarsa and quincampoix nonlinear differential equations appl 17 2010 pp 715 728 our approach embeds their idea of time change into a bsde analysis we also provide an elementary counterexample which shows that in general for the case that v solves an hjb equation with a lower obstacle the semiconcavity doesn t hold true

ends of locally symmetric spaces with maximal bottom spectrum let x be a symmetric space of non compact type and gnx a locally sym metric space then the bottom spectrum l1 gnx satisfies the inequality l1 gnx e l1 x we show that if equality l1 gnx l1 x holds then gnx has either one end which is necessarily of infinite volume or two ends one of infinite volume and another of finite vol ume in the latter case gnx is isometric to r 1 n endowed with a multi warped metric where n is compact

group extensions of gibbs markov maps let be an aperiodic cocycles with values in a locally compact abelian second countable group defined on an exact gibbs markov map t x x we show that the group extension t x g t x g x x x g is exact equivalent conditions for exactness are found

the necessary and sufficient conditions for stochastic differential systems with multi time state cost functional abstract from economics point of view we investigate a new optimal control problem driven by a stochastic differential equation with multi time state cost functional by constructing a series of first order adjoint equations we establish the stochastic maximum principle and sufficient optimality conditions for this new optimal control problem a constrained problem also be studied in the end we develop a near optimal control problem for a general cost functional

pseudo markov systems and infinitely generated schottky groups in this paper we extend the theory of conformal graph directed markov systems to what we call conformal pseudo markov systems these systems may have a countable infinite set of edges and unlike graph directed markov systems they may also have a countable infinite set of vertices our first goal is to develop suitable symbolic dynamics which we then use to analyze conformal pseudo markov systems by giving extensions of various aspects of the thermodynamic formalism and of fractal geometry most important by establishing the existence of a unique conformal measure along with its invariant version we obtain a generalization of bowen s formula concerning the hausdorff dimension of the limit set of a conformal pseudo markov system here we also obtain an interesting formula for the closure of the limit set finally we give some applications of our analysis to the theory of kleinian groups we show that there exists a rather exotic class of infinitely generated schottky groups of the second kind acting on d 1 dimensional hyperbolic space containing groups with limit sets of hausdorff dimension equal to any given number t leq d whereas their poincar e exponent can be less than any given positive number s t moreover we show that the dissipative part of the limit sets of these groups has further interesting properties

the first eigenvalue in a tower of coverings soit m une variete de riemann compacte et soit m i une famille d espaces de recouvrement riemanniens finis de m soit 1 m i la premiere valeur propre du laplacien sur m i on cherche l existence d une suite de i ou 1 m i est borne inferieurement

near maximum principle for general recursive utility optimal control problem in this study we introduce a general recursive utility optimal control problem driven by a fully nonlinear stochastic differential system in order to investigate pontryagin s stochastic maximum p

on nonlinear direct sequence detectors in arbitrary power limited interference communication over a waveform channel corrupted by additive white gaussian noise and by an unknown and arbitrary interference of bounded power is considered for this channel an upper bound is presented for the worst case error probability of a communication system comprising a direct sequence spread spectrum modulator and a nonlinear correlation receiver it is shown that this bound is exponentially tight as the number of chips used in the modulator becomes large this bound is evaluated for several detector nonlinearities numerical examples and comparisons to the performance of a pure gaussian noise channel are also given