lagrangian stochastic models with specular boundary condition abstract in this paper we prove the well posedness of a conditional mckean lagrangian stochastic model endowed with the specular boundary condition and further the mean no permeability condition in a smooth bounded confinement domain d this result extends our previous work 5 where the confinement domain was the upper half plane and where the specular boundary condition has been constructed owing to some well known results on the law of the passage times at zero of the brownian primitive the extension of the construction to more general confinement domain exhibits difficulties that we handle by combining stochastic calculus and the analysis of kinetic equations as a prerequisite for the study of the nonlinear case we construct a langevin process confined in d and satisfying the specular boundary condition we then use pde techniques to construct the time marginal densities of the nonlinear process from which we are able to exhibit the conditional mckean lagrangian stochastic model

phase diagrams of random field ising systems we show that the random field ising model may be tuned to obtain two distinct scenarios of phase diagram topology explicit evidence for this is presented in a numerically exact analysis in three dimensions and on a bethe lattice which allows us to investigate the effects of temperature coordination number and asymmetry in the field distribution

the adapted solution and comparison theorem for backward stochastic differential equations with poisson jumps and applications abstract this paper deals with a class of backward stochastic differential equations with poisson jumps and with random terminal times we prove the existence and uniqueness result of adapted solution for such a bsde under the assumption of non lipschitzian coefficient we also derive two comparison theorems by applying a general girsanov theorem and the linearized technique on the coefficient by these we first show the existence and uniqueness of minimal solution for one dimensional bsde with jumps when its coefficient is continuous and has a linear growth then we give a general feynman kac formula for a class of parabolic types of second order partial differential and integral equations pdies by using the solution of corresponding bsde with jumps finally we exploit above feynman kac formula and related comparison theorem to provide a probabilistic formula for the viscosity solution of a quasi linear pdie of parabolic type

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

approximation schemes for viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of applications including the calculus of variations control theory and differential games recently m g crandall and p l lions established the correct notion of generalized solutions for these equations this article discusses the convergence of general approximation schemes to this solution and gives under certain hypotheses explicit error estimates these results are then applied to obtain various representations as limits of solutions of general explicit and implicit finite difference schemes with error estimates

viscosity solutions for weakly coupled systems of first order partial differential equations abstract we consider viscosity solutions for weakly coupled systems of first order partial differential equations and apply these existence and uniqueness results to examples involving random evolutions

uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions in this paper we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions

forward backward stochastic differential equations on infinite horizon and quasilinear elliptic pdes 2019 elsevier inc a class of infinite horizon forward backward stochastic differential equations fbsdes is investigated under some monotonicity conditions the existence and uniqueness of solutions in an arbitrarily large space for fbsdes on infinite horizon is obtained the probabilistic interpretations for a large class of quasilinear elliptic partial differential equations pdes in a global space is then given by virtue of the solutions of fbsdes on infinite horizon

one dimensional random field ising model gibbs states and structure of ground states we consider the random gibbs field formalism for the ferromagnetic id dichotomous random field ising model as the simplest example of a quenched disordered system we prove that for nonzero temperatures the gibb state is unique for any realization of the external field then we prove that ast 0 the gibbs state converges to a limit a ground state for almost all realizations of the external field the ground state turns out to be a probability measure concentrated on an infinite set of configurations and we give a constructive description of this measure

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

optimal switching for ordinary differential equations we consider the problem of controlling an ordinary differential equation subject to positive switching costs and show in particular that the value functions form the viscosity solution cf 6 7 of the dynamic programming quasi variational inequalities this interpretation allows for a rigorous application of various dynamic programming techniques

backward stochastic differential equations on manifolds the problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering bsdes with a generator with quadratic growth we study here a generalization of these equations and we give uniqueness and existence results in two different frameworks using differential geometry tools applications to pdes are given including a certain class of dirichlet problems on manifolds

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

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

a viscosity solution approach to the asymptotic analysis of queueing systems we consider a system of several interconnected queues with a single class of customers and model the state xt of the system as a jump markov process the problem of interest is to estimate the large deviations behavior of the rescaled system xt ext s corresponding to large time and large excursions of the original unscaled system the techniques employed are those of the theory of viscosity solutions to hamilton jacobi equations from the point of view of large deviation theory the interesting new problem here is the treatment of the process when one or more of the queues are nearly empty since an abrupt change in the jump measure occurs from the point of view of viscosity solutions the discontinuity of the jump measure leads to nonlinear boundary conditions on domains with corners for the associated partial differential equations much of the paper is devoted to proving uniqueness of viscosity solutions for these equations and these sections are of independent interest while our use of test functions in proving the uniqueness is an adaptation of the usual technique the construction of the test functions themselves via the legendre transform is new we obtain a representation for the solution of the equation in terms of a nonstandard optimal control problem which suggests the correct integrand in the large deviation rate functional since it is the treatment of the effects due to the boundaries that is novel we devote the majority of the paper to the detailed development of a simple two dimensional system that exhibits all the essential new features however the arguments may be applied to nueueing systems that are considerably more general and we attempt to indicate this generality as well

two approximations of solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games the associated initial value problems almost never have global time classical solutions and one must deal with suitable generalized solutions the correct class of generalized solutions has only recently been established by the authors this article establishes the convergence of a class of difference approximations to these solutions by obtaining explicit error estimates analogous results are proved by similar means for the method of vanishing viscosity author

a stochastic control approach to the pricing of options we construct a stochastic control model of a portfolio in which the investor may invest in stock call options on the stock or risk free bonds he may also borrow funds we assume that the investor is attempting to maximize expected utility of total wealth at expiration of the options where the utility function is given as wealth to the power 0 1 this includes both the risk averse and risk neutral cases we allow the borrowing interest rate r to be distinct from the lending interest rate r we make two fundamental assumptions i the investor cannot achieve infinite expected utility of wealth in finite time stable markets and ii the market will set the option price to minimize the investor s maximal expected utility of wealth i e options are priced using a minimax strategy the market is stable only when r r we prove in the case r r and 1 that the minimax european call option price ft s is given as the solution of the black scholes equation ft i i 2s2fss i s fs i f 0 where i r when r i 2 1 i r when i 2 1 r and i i 2 1 if r i 2 1 r the parameter is the stock return drift and i is the stock return diffusion if r r then the call option price must by stable markets always be the black scholes price with rate r in the risk neutral 1 case we must have r r for a stable market and the option price given by the black scholes equation but with i explicit solutions are presented and the optimal portfolios and returns are also derived comparable results are obtained for american call options which can be exercised at any time up to and including the expiration date in this case the option pricing function is shown to be the solution of an obstacle problem

ldlt factorizations of adjacency matrices where d is block diagonal abstract for any symmetric matrix a over a field it is shown there is a permutation matrix p such that papt has a factorization papt ldlt where l is unit lower triangular and d is block diagonal with 1 by 1 or 2 by 2 blocks in particular for the adjacency matrix of a bipartite graph g the vertices of g may be ordered so that adj g ldlt where all diagonal blocks of d are 2 by 2 furthermore if g is a tree this factorization may be done with integer matrices

low temperature behaviour of the random field ising model a relationship is established between the ising model in a random positive and negative magnetic field on a lattice with p 1 2 at t 0 each percolation cluster gives rise to a first order transition at a different value of the field there is a significant difference in behaviour between lattices for which pc 1 2 which do not by considering the bethe lattice and allowing the coordination number to become large the results of the mean field approximation are reproduced the above considerations do not apply to a gaussian distribution of fields and the absence of a first order transition can be understood in this case since large clusters overturn for small fields there are clear indications of metastable behaviour

integer lu factorizations abstract let a be an m by n integer matrix and r rank a a necessary and sufficient condition is given for a to have an integer lu factorization and a modification of gaussian elimination is given for finding such factorizations when the first r leading principal minors are nonzero an algorithm is given for ordering the vertices of a tree with a loop at its root so that its adjacency matrix has an integer lu factorization

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

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

infinite horizon stochastic optimal control for volterra equations with completely monotone kernels abstract the aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro differential equation with completely monotone kernels where we assume that the noise enters the system when we introduce a control we start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods the application to optimal control provides other interesting results and requires a precise description of the properties of the generated semigroup the main tools consist in studying the differentiability of the forward backward system with infinite horizon corresponding with the reformulated problem and the proof of existence and uniqueness of mild solutions to the corresponding hamilton jacobi bellman hjb equation

fully nonlinear neumann type boundary conditions for first order hamilton jacobi equations we consider problems of the following type h x u u 0 in where is a smooth bounded open set in r n u is a scalar function from into r u denotes its frechet differential at x and h is a given continuous function on xr r n this equation is nothing but a general form of the classical first order hamilton jacobi equation in order to investigate existence and uniqueness questions the equation has to be complemented with a boundary condition on or on a part of we consider here for reasons described below a fully nonlinear boundary condition of the form f x u u 0 on that we describe as being of the neumann type

random field p spin glass model on regular random graphs we investigate in detail the phase diagrams of the p body j ising model with and without random fields on random graphs with fixed connectivity one of our most interesting findings is that a thermodynamic spin glass phase is present in the three body purely ferromagnetic model in random fields unlike for the canonical two body interaction random field ising model we also discuss the location of the phase boundary between the paramagnetic and spin glass phases that does not depend on the change of the ferromagnetic bias the independence of the ferromagnetic bias has also been observed from the perspective of the distribution of the partition function zeros on the complex field plane this behavior is explained by a gauge transformation which shows that gauge invariant properties generically do not depend on the strength of the ferromagnetic bias for the j ising model on regular random graphs

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

bsdes with terminal conditions that have bounded malliavin derivative abstract we show existence and uniqueness of solutions to bsdes of the form y t t t f s y s z s d s t t z s d w s in the case where the terminal condition has bounded malliavin derivative the driver f s y z is assumed to be lipschitz continuous in y but only locally lipschitz continuous in z in particular it can grow arbitrarily fast in z if in addition to having bounded malliavin derivative is bounded the driver needs only be locally lipschitz continuous in y in the special case where the bsde is markovian we obtain existence and uniqueness results for semilinear parabolic pdes with non lipschitz nonlinearities we discuss the case where there is no lateral boundary as well as lateral boundary conditions of dirichlet and neumann type

remarks on hamilton jacobi equations with measurable time dependent hamiltonians on considere les equations de hamilton jacobi de la forme suivante u t h x t u u 0 dans r n 0 t ou h x t s p est continu en x s p et mesurable en t on considere une extension de la notion de solution viscosite au cas de h mesurable dependant du temps

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

nested range conditions for lu factorizations of integer matrices necessary and sufficient conditions are given for an integer matrix a to have an integer lu factorization that is a factorization a lu where l and u are integer lower and upper triangular matrices respectively the possibilities of computing such factorizations with integer gaussian elimination are discussed gaussian elimination may be used to obtain an lu factorization of any rectangular matrix a over a field provided that one interchanges rows and columns of a to obtain nonzero pivots thus one actually obtains an lu factorization of paq for some permutation matrices p and q under what conditions will a matrix have an lu factorization if such permutation matrices are not used in 3 the authors considered n x n matrices a over the complex field and gave necessary and sufficient range type conditions for a to be factored as lu with all diagonal entries of u equal to 1 we generalize this result to matrices over the integers in l we considered m x n integer matrices a where rank a r and the first r leading principal minors of a are nonzero necessary and sufficient conditions on the pivots were given for a to have various types of integer ldu factorizations and a modification of gaussian elimination was presented for finding such factorizations when they exist an algorithm was also given for ordering the vertices of a tree with a loop at its root so that its adjacency matrix has an integer lu factorization in 2 we proved that in

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

a remark on a system of inequalities with bilateral obstacles up x k s up x i up l x k x e sz apup fp if up x k up x up x k x e q apup 5 fp if up x up l x k x e l2 1 1 apup l f if up x up x k x e q u x 0 onaq p 1 2 m where p ranges over 1 m and urn represents u is dealt with by the second author in 5 and the existence of a weak solution of 1 1 is established under the assumption ap s have sufficiently large zeroth order coefficients 1 2 the proof of the existence result in 5 is based on the iv estimate independent of e for the solution u 124 u of the following approximate system apu u p uf l k u k uf f in r 1 3 u 0 0naq p 1 2 m where p ranges over 1 ml p is the so called penalty function and uf represents u the gradient estimate for solutions u of 1 3 in 5 is obtained by using bernstein s method and assumption 1 2 is solely employed to make it possible in addition it should be remarked that standard variants of the bernstein trick like in 2 and 4 which are useful to obtain the iv estimate for solutions of the system of variational inequalities with unilateral constraints without 1 2 do not work in our case

the maximum principle for viscosity solutions of fully nonlinear second order partial differential equations we prove that viscosity solutions in w1 of the second order fully nonlinear equation f d2u du u 0 are unique when i f is degenerate elliptic and decreasing in u or ii f is uniformly elliptic and nonincreasing in u we do not assume that f is convex the method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions respectively this method is completely different from that used in lions 8 9 for second order problems with f convex in d 2 u and from that used by crandall lions 3 and crandall evans lions 2 for fully nonlinear first order problems

representation of solutions of hamilton jacobi equations on etudie le probleme de cauchy pour l equation de hamilton jacobi u t h t x du 0 dans o t r n avec la condition initiale u o x u o x pour x r n on a t 0 hi o t r n r n r et u o r n r sont donnes on represente la solution viscosite comme la fonction valeur d un jeu differentiel approprie

a regularity result for viscosity solutions of hamilton jacobi equations in one space dimension on demontre que dans le cas particulier d un probleme stationnaire a une dimension sous des hypotheses tres generales les solutions viscosite continues de lipschitz ont des derivees a droite et a gauche en chaque point

forward backward stochastic differential equations and quasilinear parabolic pdes this paper studies under some natural monotonicity conditions the theory existence and uniqueness a priori estimate continuous dependence on a parameter of forward backward stochastic differential equations and their connection with quasilinear parabolic partial differential equations we use a purely probabilistic approach and allow the forward equation to be degenerate

viscosity solutions of hamilton jacobi equations with unbounded nonlinear terms abstract the aim of this paper is to introduce a new definition of viscosity solutions for hamilton jacobi equations in infinite dimensions with unbounded nonlinear terms we prove existence and uniqueness results under usual assumptions regarding the bounded part of the hamiltonian

stability of bsdes with random terminal time and homogenization of semilinear elliptic pdes in this paper we extend the probabilistic method for homogenization of semi linear parabolic pdes developed by buckdahn hu and peng to the case of elliptic pdes first we give a stability result for bsdes with random terminal time which are related to elliptic pdes as shown in peng stochastics stochastics rep 37 1991 61 74 in the one dimensional case we also partially relax the monotonicity assumption on the coefficient then we use these stability results for bsdes with random terminal time to study homogenization of systems of semilinear elliptic pdes

backward stochastic differential equations with constraints on the gains process we consider backward stochastic differential equations with convex constraints on the gains or intensity of noise process existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is lipschitz continuous in the state and gains processes and convex in the gains process it is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control type equation this representation is related to the penalization method for constructing solutions of stochastic differential equations involves change of measure techniques and employs notions and results from convex analysis such as the support function of the convex set of constraints and its various properties

constructing gamma martingales with prescribed limit using backwards sde let v w and v y be euclidean vector spaces and let v z l v w v y given a wiener process w on v w with natural filtration z t and a z t measurable random variable u in v y we seek adapted processes y z in v y x v z satisfying the sde u y t t t zdw t t y zz ds 2 0 t t under local lipschitz and convexity conditions on the map y a y a these conditions apply in particular in the case y a i jk y a jk where is a linear connection on v y whose christoffel symbols i jk are bounded and lipschitz and has certain convexity properties in that case the solution y above is known as a martingale with terminal value u the solution y z is constructed explicitly using the pardoux peng theory of backwards sde s applications include the dirichlet problem and the heat equation for harmonic mappings and other pde s

probabilistic approach to singular perturbations of semilinear and quasilinear parabolic pdes in 5 buckdahn et al study some homogenization properties of systems of semilinear parabolic partial di erential equations pdes in short with periodic structures using a probabilistic approach involving stability of backward stochastic di erential equations bsdes this method is also developed in 3 to take into account systems of semilinear elliptic pdes which are related to bsdes with random terminal time moreover buckdahn and hu in 4 deal with homogenization of quasilinear pdes showing o some kind of stability property of forward backward stochastic di erential equations fbsdes in short in this paper we adopt the same method in order to study singular perturbations of semilinear pdes as well as those of quasilinear pdes the strong stability properties of bsdes allow us to study the asymptotic behavior of the solution of a system of singularly perturbed semilinear pdes by using the nonlinear feynman kac formula developed by pardoux and peng 11 singular perturbations of quasi linear pdes are treated in the same way in view of their connections to fbsdes revealed by ma et al 13

generalized viscosity solutions for hamilton jacobi equations with time measurable hamiltonians the objective of this paper is to extend the idea of viscosity solution for nonlinear first order hamilton jacobi equations u h t x d u 0 with time continuous h to time measurable hamiltonians we are primarily motivated by the fact that control problems for which the value function is the viscosity solution of a hamilton jacobi equation should not be restric ted to continuity in time in barron and jensen 1 we were confronted with a linear hamilton jacobi equation arising in the proof of the pon tryagin which had time measurable coeflicients the existing theory of viscosity solutions did not apply to even this case moreover important models of controlled first order hamiltonjacobi equations require time measurable controls for example models of controlled traffic flow or queueing processes might be of this type we are about then to extend the definition of viscosity solution to generalized viscosity solution applying to time measurable hamiltonians in this paper we give the definition and derive the corresponding uni queness result with an implicit domain of dependence consequent the fun damental technique used in the proof is the so called blow up method which has also been used elsewhere s although not in the generality discussed here this method effectively freezes the point to x0 under consideration and essentially removes it from the problem of course t is

existence of viscosity solutions of hamilton jacobi equations abstract equations of hamilton jacobi type arise in many areas of application including the calculus of variations control theory and differential games recently m g crandall and p l lions trans amer math soc 277 1983 1 42 introduced the class of viscosity solutions of these equations and proved uniqueness within this class this paper discusses the existence of these solutions under assumptions closely related to the ones which guarantee the uniqueness

bsdes driven by g brownian motion with time varying lipschitz condition abstract the present paper is devoted to the study of backward stochastic differential equations driven by g brownian motion g bsdes with time varying lipschitz condition with the help of nonlinear stochastic analysis technique and approximation method we prove that the g bsdes admit a unique solution on finite or infinite time horizon furthermore we obtain the corresponding comparison theorem

random field ising model on complete graphs and trees we present exact results for the critical behaviour of the random field ising model on complete graphs and trees both at equilibrium and away from equilibrium i e models for hysteresis and barkhausen noise we show that for stretched exponential and power law distributions of random fields the behaviour on complete graphs is non universal while the behaviour on cayley trees is universal even in the limit of large co ordination

backwards sde with random terminal time and applications to semilinear elliptic pde suppose im t is the filtration induced by a wiener process w in r d tau is a finite im t stopping time terminal time xi is an im tau measurable random variable in r k terminal value and f cdot y z is a coefficient process depending on y in r k and z in l r d r k satisfying y tilde y f s y z f s tilde y z leq a y tilde y 2 f need not be lipschitz in y and f s y z f s y tilde z leq b z tilde z for some real a and b plus other mild conditions we identify a hilbert space depending on tau and on the number gamma equiv b 2 2a in which there exists a unique pair of adapted processes y z satisfying the stochastic differential equation dy s 1 s leq tau z s dw s f s y s z s ds with the given terminal condition y tau xi provided a certain integrability condition holds this result is applied to construct a continuous viscosity solution to the dirichlet problem for a class of semilinear elliptic pde s

backward doubly stochastic equations with jumps and comparison theorems abstract in this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts several comparison theorems under some weak conditions are also given finally we apply comparison theorems in proving the existence of solution to some special backward doubly stochastic differential equations with drift coefficient increasing linearly

stochastic control for a class of nonlinear kernels and applications we consider a stochastic control problem for a class of nonlinear kernels more precisely our problem of interest consists in the optimization over a set of possibly non dominated probability measures of solutions of backward stochastic differential equations bsdes since bsdes are non linear generalizations of the traditional linear expectations this problem can be understood as stochastic control of a family of nonlinear expectations or equivalently of nonlinear kernels our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting which we then use to provide a semimartingale characterization of the value function we next explore several applications of our results we first obtain a wellposedness result for second order bsdes as introduced in 76 which does not require any regularity assumption on the terminal condition and the generator then we prove a non linear optional decomposition in a robust setting extending recent results of 63 which we then use to obtain a superhedging duality in uncertain incomplete and non linear financial markets finally we relate under additional regularity assumptions the value function to a viscosity solution of an appropriate path dependent partial differential equation ppde

hilbert space valued forward backward stochastic differential equations with poisson jumps and applications in this paper we study a class of hilbert space valued forward backward stochastic differential equations fbsdes with bounded random terminal times more precisely the fbsdes are driven by a cylindrical brownian motion on a separable hilbert space and a poisson random measure in the case where the coefficients are continuous but not lipschitz continuous we prove the existence and uniqueness of adapted solutions to such fbsdes under assumptions of weak monotonicity and linear growth on the coefficients existence is shown by applying a finite dimensional approximation technique and the weak convergence theory we also use these results to solve some special types of optimal stochastic control problems

an asymptotic formula for solutions of hamilton jacobi bellman equations on demontre que la solution de l equation de hamilton jacobi bellman converge exponentiellement vers 0 quand e 0 avec un taux de decroissance i x 0 1 e et on donne une formule de representation pour i x

the pontryagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations on demontre le principe de maximum de pontryagin pour le probleme de lagrange de commande optimale en utilisant le fait que la fonction valeur du probleme est la solution viscosite de l equation de hamilton jacobi bellman associee

lp solutions of infinite time interval backward doubly stochastic differential equations under monotonicity and general increasing conditions abstract in this paper we study the existence and uniqueness theorem for l p 1 p 2 solutions to a class of infinite time interval backward doubly stochastic differential equations bdsdes for short under monotonicity and general increasing conditions furthermore we obtain the comparison theorem for 1 dimensional infinite time interval bdsdes in l p 1 p 2

on existence and uniqueness of solutions of hamilton jacobi equations abstract the theory of scalar first order nonlinear partial differential equations has been enjoying a rapid development in the last few years this development occurred because the authors established uniqueness criteria for generalized solutions called viscosity solutions which correctly identify the solutions sought in areas of application including control theory differential games and the calculus of variations the concept of viscosity solutions is relatively easy to work with and many formally heuristic or difficult proofs have been made rigorous or simple using this concept a feedback process has begun and the experience recently gained in working with viscosity solution has suggested new existence and uniqueness results the current paper continues this interaction by establishing new existence ane uniqueness results in a natural generality suggested by earlier proofs it is also felt that the presentation of the comparison results which imply uniqueness continuous dependence and are used to estimate moduli of continuity has something to offer over earlier presentations in special cases author

the necessary conditions for optimal control in hilbert spaces obtention du principe maximum de pontryagin pour une classe generale de problemes de commande de type lagragien afin qu associe avec un ensemble de conditions necessaires une commande soit satisfaite le principe est demontre en utilisant la programmation dynamique et l equation resultante d hamilton jacobi bellman de dimension finie

perturbed dynamical systems with an attracting singularity and weak viscosity limits in hamilton jacobi equations nous donnons une nouvelle preuve par des methodes edp du theoreme de wentzell freidlin concernant les petites perturbations d un systeme dynamique l e u e e 2 u e b u e 0 dans u e sur nous prouvons que si b a un seul point singulier attractif alors u e converge vers une constante uniformement sur tout compact et avec une vitesse exponentielle nous determinons nous traitons aussi le cas de conditions aux limites de neumann pour cela nous faisons l analyse asymptotique d une mesure ergodique intervenant naturellement dans le probleme ce qui revient a etudier la limite par viscosite evanescente dans une equation de hamilton jacobi

inherited lu factorizations of matrices various types of lu factorizations for nonsingular matrices where l is a lower triangular matrix and u is an upper triangular matrix are defined and characterized these types of lu factorizations are extended to the general m n case the more general conditions are considered in the light of the structures of c r johnson d d olesky p van den driessche inherited matrix entries lu factorizations siam j matrix anal appl 10 1989 99 104 applications to graphs and adjacency matrices are investigated conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained

infinite horizon bsdes with dissipative coefficients in hilbert spaces and applications in this paper we study a class of infinite horizon backward stochastic differential equations bsdes of the form dy t y t dt f t y t z t dt z t dw t 0 t in a real separable hilbert space where is a given real parameter and the coefficient f is dissipative in y and lipschitz in z by yosida approximation to dissipative mappings we show existence and uniqueness of the solutions for these equations this result is applied to construct unique viscosity solutions to semilinear elliptic partial differential equations pdes

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

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