existence of solutions of nonlinear stochastic integrodifferential inclusions in a hilbert space in this paper the existence of mild solutions of nonlinear stochastic integrodifferentialinclusions in a hilbert space is studied the results are obtained by using a fixed point theorem for condensing map due to martelli the result is illustrated with an example

yosida approximations for multivalued stochastic partial differential equations driven by levy noise on a gelfand triple abstract we prove the existence and uniqueness of solutions for a class of multivalued stochastic partial differential equations with maximal monotone drift on banach space driven by multiplicative levy noise we also establish the strong convergence result for solutions of the approximating equations where the maximal monotone drift operator is replaced by its yosida approximation as an application the existence and uniqueness of solutions for multivalued stochastic porous medium equations is obtained

controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space abstract in this paper sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the leray schauder nonlinear alternative an example is provided to illustrate the theory

asymptotic couplings by reflection and applications for nonlinear monotone spdes abstract asymptotic couplings by reflection are constructed for a class of nonlinear monotone spdes stochastic partial differential equations as applications gradient holder estimates as well as exponential convergence are derived for the associated markov semigroup the main results are illustrated by stochastic generalized porous media equations stochastic p laplacian equations and stochastic generalized fast diffusion equations we emphasize that the gradient estimate is studied for the first time for these equations

on a stochastic evolution equation in a real separable hilbert space h where for every f 30 a t da c h h is a linear possibly unbounded operator v r 1a0 is a hilbert valued process of bounded variation m t a 0 is a hilbert valued locally square integrable martingale z t a o is a hilbert valued semimartingale and b c are operator valued functionals on the set of cadlag adapted hvalued processes b may be multivalued particular cases of i have been studied by many authors for example by arnold curtain kotelenez 11 chojnowska michalik 2 daletskii 4 da prato iannelli tubaro s 61 gyongy s ichikawa 9 lo kotelenez 14 151 krte 16 mahno 17 metivier 18 metivier pellaumail 193 metivier pistone 120 211 tubaro 23 tudor 24 25 krylov rozovskii 27 we propose conditions which insure the existence and the pathwise uniqueness for the mild solutions of i

stochastic variational inequalities on non convex domains abstract the objective of this work is to prove in a first step the existence and the uniqueness of a solution of the following multivalued deterministic differential equation d x t x t d t d m t t 0 x 0 x 0 where m r r d is a continuous function and is the frechet subdifferential of a semiconvex function the domain of can be non convex but some regularities of the boundary are required the continuity of the map m x c 0 t r d c 0 t r d associating to the input function m the solution x of the above equation as well as tightness criteria allows to pass from the above deterministic case to the following stochastic variational inequality driven by a multi dimensional brownian motion x t k t 0 t f s x s d s 0 t g s x s d b s t 0 d k t x t d t

the interrelation between stochastic differential inclusions and set valued stochastic differential equations abstract in this paper we connect the well established theory of stochastic differential inclusions with a new theory of set valued stochastic differential equations solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty bounded convex and closed subsets of the space l 2 consisting of square integrable random vectors we show that for the solution x to a set valued stochastic differential equation corresponding to a stochastic differential inclusion there exists a solution x for this inclusion that is a l 2 continuous selection of x this result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions as well as to consider the viability problem for stochastic differential inclusions

on stochastic evolution equations for nonlinear bipolar fluids well posedness and some properties of the solution abstract we investigate the stochastic evolution equations describing the motion of a non newtonian fluids excited by multiplicative noise of levy type we show that the system we consider has a unique global strong solution we also give some results concerning the properties of the solution we mainly prove that the unique solution satisfies the markov feller property this enables us to prove by means of some results from ergodic theory that the semigroup associated to the unique solution admits at least an invariant measure which is ergodic and tight on a subspace of the lebesgue space l 2

second order multivalued stochastic differential equations on riemannian manifolds the existence and uniqueness of solutions to multivalued stochastic differential equations of the second order on riemannian manifolds are proved the class of problem is motivated by rigid body and multibody dynamics with friction and an application to the spherical pendulum with friction is presented

lp strong convergence of the averaging principle for slow fast spdes with jumps abstract the averaging principle is an important method to extract effective macroscopic dynamic from complex systems with slow component and fast component this paper concerns the l p strong convergence of the averaging principle for two time scales stochastic partial differential equations spdes driven by wiener processes and poisson jumps to achieve this a key step is to show the existence for an invariant measure with exponentially ergodic property for the fast equation where the dissipative conditions are needed furthermore it is shown that under suitable assumptions the slow component l p strongly converges to the solution of the averaged equation the rate of the convergence is also obtained as a byproduct

liouville theorems for non local operators abstract the paper characterizes some classes of pseudo differential operators for which there are or there are not non constant bounded harmonic functions non local perturbations of ornstein uhlenbeck operators and operators with dissipative coefficients are considered the methods used are probabilistic and based on the concept of absorption function and on a new extension of the bismut elworthy li formula the probabilistic interpretation of the liouville theorem by means of absorption functions for general markov processes is given as well

nonlinear random equations involving operators of monotone type the systematic study of random equations has been initiated by spaeek 19 and hans 9 in recent years kannan and salehi 13 and itoh 111 have treated nonlinear random equations with monotone operators in 14 151 the author studied nonlinear random equations and inequalities with singlevalued or multivalued operators of monotone type it is the purpose of this paper to give some new existence theorems for nonlinear random equations with operators of monotone type more precisely in section 3 we present an existence and perturbation theory for solutions of nonlinear random equations involving multivalued maximal monotone operators in section 4 we study a random hammerstein equation in a hilbert space involving a closed linear maximal monotone random operator and a random operator of type m in section 5 we consider random equations with noncoercive pseudomonotone operators instead of coercivity a leray schauder type boundary condition is assumed

diffusion equation for multivalued stochastic differential equations abstract deterministic oscillations with bilinear hysteresis are governed by a multivalued differential equation of the type k b g where k is maximal monotonic and b is lipschitzian an existence and uniqueness result is proven for corresponding stochastic equation the diffusion equation satisfied by the laws of t is established in the particular case k 0 this equation is equivalent to the fokker planck equation

stochastic porous media equations and self organized criticality the existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and wiener forcing term is proven the finite time extinction of solutions with high probability is also proven in 1 d the results are relevant for self organized criticality behavior of stochastic nonlinear diffusion equations with critical states

spde in hilbert space with locally monotone coefficients the aim of this paper is to extend the usual framework of spde with monotone coecients to include a large class of cases with merely locally monotone coecients this new framework is conceptually not more involved than the classical one but includes many more fundamental examples not included previously thus our main result can be applied to various types of spdes such as stochastic reaction diusion equations stochastic burgers type equation stochastic 2 d navier stokes equation stochastic p laplace equation and stochastic porous media equation with non monotone perturbations

schauder estimates for stochastic transport diffusion equations with levy processes abstract in this study we consider a transport diffusion equation with levy noise and holder continuous coefficients by using the heat kernel estimates we derive the schauder estimates for the mild solutions moreover when the transport term vanishes and p 2 we show that the holder index in the space variable is optimal

strong feller property and irreducibility for diffusions on hilbert spaces it is shown that the transition semigroup p t t 0 corresponding to a nonlinear stochastic evolution equation is strong feller and irreducible provided the nonlinearities are lipschitz continuous and the diffusion term is nondegenerate this result ensures the uniqueness of the invariant measure for p t t 0

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

second order hamilton jacobi bellman equations with an unbounded operator abstract this work is devoted to the study of a class of hamilton jacobi bellman equations associated to an optimal control problem where the state equation is a stochastic differential inclusion with a maximal monotone operator we show that the value function minimizing a bolza type cost functional is a viscosity solution of the hjb equation the proof is based on the perturbation of the initial problem by approximating the unbounded operator finally by providing a comparison principle we are able to show that the solution of the equation is unique

nonlinear random equations with noncoercive operators in banach spaces admits random solutions in 121 itoh proved the existence of solutions of nonlinear random equations with monotone operators his method of proving the measurability of solutions was based on the selection theorem of kuratowski and ryll nardzewski 16 in 13 141 itoh s method was extended to obtain existence theorems for nonlinear random equations and inequalities with single valued or multivalued operators of monotone type the above results were derived under the basic assumption that the random operators are coercive it is the purpose of this paper to give some new existence results concerning the solvability of nonlinear random equations with noncoercive operators as in the coercive case the measurability of solutions depends mainly on the selection theorem proved in 161 in section 3 we prove the existence of solutions of nonlinear random equations with multivalued operators satisfying a leray schauder type boundary condition generalizing thus some results in 151 in section 4 we study the solvability of the random equation

bmo and morrey campanato estimates for stochastic convolutions and schauder estimates for stochastic parabolic equations abstract in this paper we are aiming to prove several regularity results for the following stochastic fractional heat equations with additive noises d u t x 2 u t x d t g t x d t u 0 0 t 0 t x g for a random field u t x 0 t g u t x u t x r where 2 2 0 2 is the fractional laplacian t 0 is arbitrarily fixed g r d is a bounded domain g 0 t g r is a joint measurable coefficient and t t 0 is either a brownian motion or a levy process on a given filtered probability space f p f t t 0 t to this end we derive the bmo estimates and morrey campanato estimates respectively for stochastic singular integral operators arising from the equations concerned then by utilizing the embedding theory between the campanato space and the holder space we establish the controllability of the norm of the space c 2 d where 0 d 0 t g with all these in hand we are able to show that the q th order bmo quasi norm of the q 0 order derivative of the solution u is controlled by the norm of g under the condition that t is a levy process finally we derive the schauder estimate for the p moments of the solution of the above stochastic fractional heat equations driven by levy noise

invariance of closed convex cones for stochastic partial differential equations abstract the goal of this paper is to clarify when a closed convex cone is invariant for a stochastic partial differential equation spde driven by a wiener process and a poisson random measure and to provide conditions on the parameters of the spde which are necessary and sufficient

the stochastic reflection problem with multiplicative noise abstract this paper addresses the existence and uniqueness of strong solutions to the stochastic variational inequality d x x d t f t x d t x d t k 1 m x k d k t f t d t in a bounded domain o r d with dirichlet homogeneous conditions here r 0 for r 0 0 0 r 0 for r 0 an application to the one phase stefan problem with a stochastic heat source is given one studies also the corresponding stochastic parabolic equation with signorini boundary conditions x x 0 on o

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

stochastic nonlinear wave equation with memory driven by compensated poisson random measures in this paper we study a class of stochastic nonlinear wave equation with memory driven by levy noise we first show the existence and uniqueness of global mild solutions using a suitable energy function second under some additional assumptions we prove the exponential stability of the solutions

stochastic generalized porous media and fast diffusion equations abstract we present a generalization of krylov rozovskii s result on the existence and uniqueness of solutions to monotone stochastic differential equations as an application the stochastic generalized porous media and fast diffusion equations are studied for finite reference measures where the drift term is given by a negative definite operator acting on a time dependent function which belongs to a large class of functions comparable with the so called n functions in the theory of orlicz spaces

well posedness and invariant measures for a class of stochastic 3d navier stokes equations with damping driven by jump noise abstract a class of stochastic 3d navier stokes equation with damping driven by a noise of levy type is considered in this paper the existence and uniqueness of the solution for the problem 1 1 1 2 are proved for 2 with any 0 and 1 4 as 2 the main result covered various types of spde such as stochastic 3d navier stokes equations with damping stochastic tamed 3d navier stokes equations stochastic three dimensional brinkman forchheimer extended darcy model by using the exponential stability of solutions the existence of a unique invariant measures is proved

robustness in stable generalized finite element methods sgfem applied to poisson problems with crack singularities abstract in this paper we study the performance of the generalized finite element method gfem applied to the poisson problem with crack singularities recently a gfem with modified heaviside enrichments was proposed in gupta et al 2013 to approximate the solution of a 2d elasticity problem with a crack it was shown that the gfem is indeed a stable gfem sgfem i e it yields the optimal order of convergence and its conditioning is not worse than that of the standard finite element method fem however the robustness of the conditioning of the gfem with respect to the position of the mesh relative to the crack was not addressed in gupta et al 2013 in this paper we observed that the conditioning of the gfem with the enrichments used in gupta et al 2013 is not robust when applied to approximate the solution of the poisson problem moreover the order of convergence may not be optimal when the position of the mesh is changed with respect to the crack interfaces we proposed using additional singular enrichments at the nodes close to the crack near the crack tip we proved that the gfem with enrichments proposed in this paper yields optimal order of convergence irrespective of the position of the mesh moreover with a local orthogonalization procedure we have shown through numerical experiments that the conditioning of this gfem is not worse than that of the standard fem and the conditioning is robust with respect to the position of the mesh thus the gfem with the enrichments suggested in this paper is indeed an sgfem when applied to a poisson problem with the crack singularities

stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise in this work we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation rm d x t rm div left frac nabla x t nabla x t right rm d t x t rm d w t rm in 0 infty times mathcal o where mathcal o is a bounded and open domain in mathbb r n n geqq 1 and w t is a wiener process of the form w t sum infty k 1 mu k e k beta k t e k in c 2 overline mathcal o cap h 1 0 mathcal o and beta k k in mathbb n are independent brownian motions this is a stochastic diffusion equation with a highly singular diffusivity term one main result established here is that for all initial conditions in l 2 mathcal o it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality thus one obtains a stochastic version of the minimal total variation flow the new approach developed here also allows us to prove the finite time extinction of solutions in dimensions 1 leqq n leqq3 which is another main result of this work

online removable knapsack problem under convex function abstract in this paper we address an online knapsack problem under a convex size profit function we first give a greedy online algorithm with a competitive ratio 2 then we propose an improved online algorithm with a competitive ratio 5 3 we also prove that when the convex function has a specific property our improved online algorithm is 1 5 2 competitive which is optimal finally we prove that the lower bound of this problem is 1 5 2

online knapsack problem under concave functions in this paper we address an online knapsack problem under concave function f x i e an item with size x has its profit f x we first obtain a simple lower bound max q frac f 0 f 1 where q approx 1 618 then show that this bound is not tight and give an improved lower bound finally we find the online algorithm for linear function 8 can be employed to the concave case and prove its competitive ratio is frac f 0 f 1 q then we give a refined online algorithm with a competitive ratio frac f 0 f 1 1 and we also give optimal algorithms for some piecewise linear functions

stochastic maximal lp regularity in this article we prove a maximal lp regularity result for stochastic convolutions which extends krylov s basic mixed lp lq inequality for the laplace operator on d to large classes of elliptic operators both on d and on bounded domains in d with various boundary conditions our method of proof is based on mcintosh s h functional calculus r boundedness techniques and sharp lp lq square function estimates for stochastic integrals in lq spaces under an additional invertibility assumption on a a maximal space time lp regularity result is obtained as well

self organization and anomalous diffusion abstract the self organizing process is investigated in the continuum limit of the cellular automaton model introduced by bak tang and wiesenfeld an anomalous diffusion equation is proposed for the description of this process and an analytical method for the solutionis presented in one dimension based on an adiabatic approximation

ultraboundedness for parabolic equations in convex domains without boundary conditions abstract we consider the operator a u 1 2 u d u d u where u is a convex real function defined in a convex open set o r n and lim x u x lim x o u x we prove that the associated markov semigroup is ultrabounded with respect to the gibbs measure e 2 u x d x

proportional cost buyback problem with weight bounds abstract in this paper we study the proportional cost buyback problem the input is a sequence of elements e 1 e 2 e n each of which has a weight w e i we assume that weights have an upper and a lower bound i e l w e i u for any i given the ith element e i we either accept e i or reject it with no cost subject to some constraint on the set of accepted elements during the iterations we could cancel some previously accepted elements at a cost that is proportional to the total weight of them our goal is to maximize the profit i e the sum of the weights of elements kept until the end minus the total cancellation cost occurred we consider a matroid and the unweighted knapsack constraints for either case we construct optimal online algorithms and prove that they are the best possible

regular dependence on initial data for stochastic evolution equations with multiplicative poisson noise abstract we prove existence uniqueness and lipschitz dependence on the initial datum for mild solutions of stochastic partial differential equations with lipschitz coefficients driven by wiener and poisson noise under additional assumptions we prove g teaux and frechet differentiability of solutions with respect to the initial datum as an application we obtain gradient estimates for the resolvent associated to the mild solution finally we prove the strong feller property of the associated semigroup

large deviations of max weight scheduling policies on convex rate regions we consider a single server discrete time system with a fixed number of users where the server picks operating points from a compact convex and coordinate convex set for this system we analyse the performance of a stabilising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rates where the weights depend on the work loads of the users assuming a large deviations principle ldp for the arrival processes in the skorohod space of functions that are right continuous with left hand limits we establish an ldp for the work load process using a generalised version of the contraction principle to derive the corresponding rate function with the ldp result available we then analyse the tail probabilities of the work loads under different buffering scenarios

irregular convergence of mild solutions of semilinear equations abstract we prove that even irregular convergence of semigroups of operators implies similar convergence of mild solutions of the related semi linear equations with lipschitz continuous nonlinearity this result is then applied to three models originating from mathematical biology shadow systems diffusions on thin layers and dynamics of neurotransmitters

2d stochastic navier stokes equations driven by jump noise abstract in the paper we are studying the existence and uniqueness of the solution of an abstract nonlinear equation driven by a multiplicative noise of levy type our result is formulated in an abstract setting this type of equation covers the stochastic 2d navier stokes equations the 2d stochastic magneto hydrodynamic equations the 2d stochastic boussinesq model for the benard convection the 2d stochastic magnetic bernard problem the 3d stochastic leray model for the navier stokes equations and several stochastic shell models of turbulence

finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise abstract in this paper one surveys and sharpens some recent results obtained by the authors on the finite time extinction property of solutions to stochastic diffusion equations of the form d x x m d t x d w and d x sgn x d t x d w where 0 m 1 0 these equations arise as models for nonlinear diffusion processes in porous media plasma and self organized criticality under stochastic gaussian perturbation these equations can be also viewed as control systems governed by fast diffusion porous media equations with a stochastic feedback controller x d w

the optimal control problem associated with multi valued stochastic differential equations with jumps abstract this work concerns the optimal control problem associated with multi valued stochastic differential equations with levy jumps through the yosida approximation technique we prove that the value function of the control problem is the unique viscosity solution of a second order parabolic integro differential equation involving a multi valued maximal monotone operator the dynamic programming principle and the comparison theorem are also proved

deterministic and stochastic differential inclusions with multiple surfaces of discontinuity we consider a class of deterministic and stochastic dynamical systems with discontinuous drift f and solutions that are constrained to live in a given closed domain g in mathbb r n according to a constraint vector field d specified on the boundary partial g of the domain specifically we consider equations of the form phi theta eta u quad dot theta t in f phi t quad mbox a e t for u in an appropriate class of functions where is the constraining term in the skorokhod problem specified by g d and f is the set valued upper semicontinuous envelope of f the case g mathbb r n when there is no constraining mechanism and u is absolutely continuous corresponds to the well known setting of differential inclusions di we provide a general sufficient condition for uniqueness of solutions and lipschitz continuity of the solution map in the form of existence of a lyapunov set here we assume i g is convex and admits the representation g cup i overline c i where c i i in mathbb i is a finite collection of disjoint open convex polyhedral cones in mathbb r n each having its vertex at the origin ii f b f c is a vector field defined on g such that b assumes a constant value on each of the given cones and f c is lipschitz continuous on g and iii d is an upper semicontinuous cone valued vector field that is constant on each face of g we also provide existence results under much weaker conditions where no lyapunov set condition is imposed for stochastic differential equations sde possibly reflected that have drift coefficient f and a lipschitz continuous possibly degenerate diffusion coefficient we establish strong existence and pathwise uniqueness under appropriate conditions our approach yields new existence and uniqueness results for both di and sde even in the case g mathbb r n the work has applications in the study of scaling limits of stochastic networks

probleme de skorohod multivoque on prouve un resultat d existence et d unicite pour une generalisation par introduction d un operateur maximal monotone multivoque du probleme de skorohod avec reflexion normale deterministe associe a un convexe ferme d de r d la formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine cette approche multivoque clarifie la connexion entre probleme de skorohod et semigroupes nonlineaires en guise d application on considere ensuite le cas stochastique les equations differentielles stochastiques multivoques sont ainsi revisitees par consequent cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu explosif

an algebraic multigrid approach to solve extended finite element method based fracture problems summary this article proposes an algebraic multigrid amg approach to solve linear systems arising from applications where strong discontinuities are modeled by the extended finite element method the application of amg methods promises optimal scalability for solving large linear systems however the straightforward or black box use of existing amg techniques for extended finite element method problems is often problematic in this paper we highlight the reasons for this behavior and propose a relatively simple adaptation that allows one to leverage existing amg software mostly unchanged numerical tests demonstrate that optimal iterative convergence rates can be attained that are comparable with amg convergence rates associated with linear systems for standard finite element approximations without discontinuities published 2012 this article is a us government work and is in the public domain in the usa

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

stochastic porous media equations and self organized criticality convergence to the critical state in all dimensions if x x t is the solution to the stochastic porous media equation in mathcal o subset mathbf r d 1 le d le 3 modelling the self organized criticality barbu et al in commun math phys 285 901 923 2009 and x c is the critical state then it is proved that int infty 0m mathcal o setminus mathcal o t 0 dt infty mathbb p hbox a s and lim t to infty int mathcal o x t x c d xi ell infty mathbb p hbox a s here m is the lebesgue measure and mathcal o t c is the critical region xi in mathcal o x t xi x c xi and x c x 0 a e xi in mathcal o if the stochastic gaussian perturbation has only finitely many modes but is still function valued lim t to infty int k x t x c d xi 0 exponentially fast for all compact k subset mathcal o with probability one if the noise is sufficiently strong we also recover that in the deterministic case l 0

an extended finite element method with algebraic constraints xfem ac for problems with weak discontinuities abstract we present a new extended finite element method with algebraic constraints xfem ac for recovering weakly discontinuous solutions across internal element interfaces if necessary cut elements are further partitioned by a local secondary cut into body fitting subelements each resulting subelement contributes an enrichment of the parent element the enriched solutions are then tied using algebraic constraints which enforce c 0 continuity across both cuts these constraints impose equivalence of the enriched and body fitted finite element solutions and are the key differentiating feature of the xfem ac in so doing a stable mixed formulation is obtained without having to explicitly construct a compatible lagrange multiplier space and prove a formal inf sup condition likewise convergence of the xfem ac solution follows from its equivalence to the interface fitted finite element solution this relationship is further exploited to improve the numerical solution of the resulting xfem ac linear system examples are shown demonstrating the new approach for both steady state and transient diffusion problems

existence of strong solutions for stochastic porous media equation under general monotonicity conditions this paper addresses existence and uniqueness of strong solutions to stochastic porous media equations dx x dt b x dw t in bounded domains of r d with dirichlet boundary conditions here is a maximal monotone graph in r r possibly multivalued with

multi valued stochastic differential equations driven by g brownian motion and related stochastic control problems abstractin this paper we prove the existence and uniqueness of a solution for a class of multi valued stochastic differential equations driven by g brownian motion msdeg by means of the yosida approximation method moreover we set up an optimality principle of stochastic control problem and prove the value function of the control problem is the unique viscosity solution of a class of nonlinear partial differential variational inequalities

online knapsack of unknown capacity how to optimize energy consumption in smartphones abstract we propose a new variant of the standard online knapsack problem where the only information missing to the provided instances is the capacity b of the knapsack we refer to this problem as the online knapsack of unknown capacity kuc problem any algorithm solving the kuc problem must provide a strategy for filling online the knapsack until its capacity is revealed when the knapsack capacity is revealed no other item can be inserted and also the last inserted item is discarded if it does not completely fit in the knapsack apart for the interest in a new version of the fundamental knapsack problem the motivations that lead to define this new variant come from energy consumption constraints in smartphones communications we provide lower and upper bounds to the problem for various cases in general we design an optimal algorithm admitting a 1 2 competitive ratio when all items admit uniform ratio of profit over size our algorithm provides a 49 86 569 competitive ratio that leaves some gap with the provided bound of 1 618 the inverse of the golden number we then conduct experimental analysis for the competitive ratio guaranteed algorithms compared to the optimum and to various heuristics

robust and scalable domain decomposition solvers for unfitted finite element methods abstract unfitted finite element methods e g extended finite element techniques or the so called finite cell method have a great potential for large scale simulations since they avoid the generation of body fitted meshes and the use of graph partitioning techniques two main bottlenecks for problems with non trivial geometries however the linear systems that arise from these discretizations can be much more ill conditioned due to the so called small cut cell problem the state of the art approach is to rely on sparse direct methods which have quadratic complexity and are thus not well suited for large scale simulations in order to solve this situation in this work we investigate the use of domain decomposition preconditioners balancing domain decomposition by constraints for unfitted methods we observe that a straightforward application of these preconditioners to the unfitted case has a very poor behavior as a result we propose a customization of the classical bddc methods based on the stiffness weighting operator and an improved definition of the coarse degrees of freedom in the definition of the preconditioner these changes lead to a robust and algorithmically scalable solver able to deal with unfitted grids a complete set of complex 3d numerical experiments shows the good performance of the proposed preconditioners

non monotone stochastic generalized porous media equations abstract by using the nash inequality and a monotonicity approximation argument existence and uniqueness of strong solutions are proved for a class of non monotone stochastic generalized porous media equations moreover we prove for a large class of stochastic pde that the solutions stay in the smaller l 2 space provided the initial value does so that some recent results in the literature are considerably strengthened

strong averaging principle for two time scale non autonomous stochastic fitzhugh nagumo system with jumps in this paper we study an averaging principle for stochastic fitzhugh nagumo system with different time scales driven by cylindrical wiener processes and poisson jumps where the slow equation is non autonomous and the fast equation is autonomous case under suitable assumptions we show that the slow component mean square strongly converges to the solution of the corresponding averaging equation and the rate of the convergence as a by product is also affirmed finally we give some open problems which are derived from this paper

stochastic on line knapsack problems different classes of on line algorithms are developed and analyzed for the solution of 0 1 and relaxed stochastic knapsack problems in which both profit and size coefficients are random variables in particular a linear time on line algorithm is proposed for which the expected difference between the optimum and the approximate solution value iso log3 2n an 1 lower bound on the expected difference between the optimum and the solution found by any on line algorithm is also shown to hold

existence of solutions of semilinear stochastic delay evolution inclusions in a hilbert space in this paper the existence of mild solutions of a class of semilinear stochastic evolution inclusions with delays in a hilbert space is studied the results are obtained by using a fixed point theorem for condensing map due to martelli the result is illustrated with an example

the euler scheme for levy driven stochastic differential equations in relation with monte carlo methods to solve some integro differential equations we study the approximation problem of ee g x t by ee g bar x t n where x t 0 leq t leq t is the solution of a stochastic differential equation governed by a levy process z t bar x n t is defined by the euler discretization scheme with step fractn with appropriate assumptions we show that the error ee g x t ee g bar x t n can be expanded in powers of frac1n if the levy measure of z has finite moments of order high enough otherwise the rate of convergence is slower and its speed depends on the behavior of the tails of the levy measure the simulation of the increments of z t is also discussed

successive approximation of neutral stochastic evolution equations with infinite delay and poisson jumps abstract in this paper we study the existence and uniqueness of mild solutions of neutral stochastic evolution equations with infinite delay and poisson jumps in real separable hilbert spaces we study the continuous dependence of solutions on the initial value the nonlinear term in our equations are not assumed to lipschitz continuous the results of this paper generalize and improve some known results

lq valued burkholder rosenthal inequalities and sharp estimates for stochastic integrals we prove sharp maximal inequalities for formula presented valued stochastic integrals with respect to any hilbert space valued local martingale our proof relies on new burkholder rosenthal type inequalities for martingales taking values in an formula presented space

a quasi algebraic multigrid approach to fracture problems based on extended finite elements the modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges the extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated remeshing to properly address propagation of cracks they do however give rise to linear systems requiring special care within an iterative solver method an algebraic multigrid method is proposed that is suitable for the linear systems associated with modeling fracture via extended finite elements the new method follows naturally from an energy minimizing algebraic multigrid framework the key idea is the modification of the prolongator sparsity pattern to prevent interpolation across cracks this is accomplished by accessing the standard levelset functions used during the discretization process numerical experiments illustrate that the resulting method converges in a fashion that is relatively insensitive to mesh resolution and to the number of cracks or their location

finite time extinction for stochastic sign fast diffusion and self organized criticality we prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space time noise corresponding to the bak tang wiesenfeld model for self organized criticality this solves a problem posed and left open in several works barbu methods appl sci 36 1726 1733 2013 rockner and wang j lond math soc 2 87 545 560 2013 barbu et al j math anal appl 389 147 164 2012 barbu and rockner comm math phys 311 539 555 2012 barbu et al comm math phys 285 901 923 2009 c r math acad sci paris 347 1 2 81 84 2009 the highly singular degenerate nature of the drift in interplay with the stochastic perturbation causes the need for new methods in the analysis of mass diffusion and several new estimates and techniques are introduced

approximation and convergence of solutions to semilinear stochastic evolution equations with jumps we prove that the mild solution to a semilinear stochastic evolution equation on a hilbert space driven by either a square integrable martingale or a poisson random measure is jointly continuous in a suitable topology with respect to the initial datum and all coefficients in particular if the leading linear operators are maximal quasi monotone and converge in the strong resolvent sense the drift and diffusion coefficients are uniformly lipschitz continuous and converge pointwise and the initial data converge then the solutions converge

asymptotic behavior of the nonlinear diffusion equation nt n 1nx x the asymptotic behavior of the equation nt ln n xx is studied on the finite interval 0 x 1 with the boundary conditions n 0 t n 1 t n0 and initial data n x 0 n0 we prove that asymptotically ln n x t n0 a exp 2t n0 21 2 sin x and also provide rigorous upper and lower bounds on the asymptotic amplitude a in terms of integrals of nonlinear functions of the initial data the rigorous bounds are compared to values of a obtained from computer experiments the lower bound l 23 2 exp li 1 q where li is the logarithmic integral is euler s constant and q 2 f n x 0 n0 1 sin x dx is found to be the best known estimate of a

nonlinear stochastic partial differential equations with singular diffusivity and gradient stratonovich noise abstract we study existence and uniqueness of a variational solution in terms of stochastic variational inequalities svi to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative stratonovich gradient type noise we derive a commutator relation for the unbounded noise coefficients in terms of a geometric killing vector condition the drift term is given by the total variation flow respectively by a singular p laplace type operator we impose nonlinear zero neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise this solves an open problem posed in barbu et al 2013 7 and barbu and rockner 2015 10

the two phase stochastic stefan problem this work is concerned with existence for a stochastic free boundary problem arising in phase transition the stefan two phase problem the existence of an invariant ergodic measure associated with the corresponding transition semigroup p t is also proved together with an integration by parts formula for the generator of p t

evolution problems in spaces of probability measures abstract this is a short survey paper on the application of monge s theory of optimal mass transportation to evolution problems of a gradient type in the case when the natural state space is the space of probability measures this occurs for instance for fokker planck equations and optimal mass transportation methods provide in this setting very general existence and stability results

maximal regularity for stochastic convolutions driven by levy processes we generalize the maximal regularity result from da prato and lunardi atti accad naz lincei cl sci fis mat natur rend lincei 9 mat appl 9 1 25 29 1998 to stochastic convolutions driven by time homogenous poisson random measures and cylindrical infinite dimensional wiener processes

study of a maximal monotone model with a delay term we present a model involving a friction term and a delay term by using results of existence and uniqueness for maximal monotone differential inclusions we give theoretical results for this model an implicit euler numerical scheme and results related to order of convergence are also provided from both a theoretical and a numerical point of view