theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

generalized reflected bsdes driven by a levy process and an obstacle problem for pdies with a nonlinear neumann boundary condition in this paper we derive the existence and uniqueness of the solution for a class of generalized reflected backward stochastic differential equations grbsdes in short driven by a levy process which involve the integral with respect to a continuous process by means of the snell envelope the penalization method and the fixed point theorem in addition we obtain the comparison theorem for the solutions of the grbsdes as an application we give a probabilistic formula for the viscosity solution of an obstacle problem for a class of partial differential integral equations pdies in short with a nonlinear neumann boundary condition

sur les distributions covariantes dans les algebres de lie reductives abstract we study the possibility of factoring a covariant distribution on reductive lie algebras as finite sum of products of an invariant distribution by a covariant polynomial

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

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

characters of some unitary highest weight representations via the theta correspondence abstract in this article we consider a dual pair g g in the symplectic group sp w with g compact and let g g be the preimages of g and g in the metaplectic group sp w for every irreducible representation of g appearing in howe correspondence we compute explicitly the restriction of the character of the associated representation of g on the set of regular points on the compact cartan subgroup h of g

fonctions orbitales surgc gr formule d inversion des integrales orbitales et formule de plancherel resume soitgun groupe de lie semi simple complexe connexe et simplement connexe d algebre de lie g soithune forme reelle degd algebre de lie h apres une etude generale des fonctions orbitales surg h nous construisons des series de fonctions orbitales propres sous l action de l algebre des operateurs differentielsg invariant surg h en utilisant les resultats de p harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication concernant les fonctions generalisees spheriques surg h nous demontrons la formule d inversion des integrales orbitales d une fonction de classec a support compact surg h nous en deduisons la formule de plancherel pour l espace symetriqueg h letgbe a complex connected and simply connected semisimple lie group with lie algebra g lethbe a real form ofgwith lie algebra h after a general study of orbital functions ong h we construct series of orbital functions which are eigen for the action ofg invariant differential operators ong h using the results harinck base de la serie la plus continue de fonctions generalisees spheriques surg c g r prepublication about spherical generalized functions ong h we prove the inversion formula for orbital integrals of ac function with compact support ong h we deduce the plancherel formula for the symmetric spaceg h

numerical approximation of doubly reflected bsdes with jumps and rcll obstacles we study a discrete time approximation scheme for the solution of a doubly reflected backward stochastic differential equation dbbsde in short with jumps driven by a brownian motion and an independent compensated poisson process moreover we suppose that the obstacles are right continuous and left limited rcll processes with predictable and totally inaccessible jumps and satisfy mokobodski s condition our main contribution consists in the construction of an implementable numerical sheme based on two random binomial trees and the penalization method which is shown to converge to the solution of the dbbsde finally we illustrate the theoretical results with some numerical examples in the case of general jumps

mixed zero sum stochastic differential game and american game options in this paper we solve the mixed zero sum stochastic differential game problem in the general case the main tool is the notion of a local solution of backward stochastic differential equations bsdes with two reflecting barriers as an application we deal with the american game options

on the equality of solutions of max min and min max systems of variational inequalities with interconnected bilateral obstacles abstract in this paper we deal with the solutions of systems of pdes with bilateral interconnected obstacles of min max and max min types these systems arise naturally in stochastic switching zero sum game problems we show that when the switching costs of one side are regular the solutions of the min max and max min systems coincide then this common viscosity solution is related to a multi dimensional doubly reflected bsde with bilateral interconnected obstacles finally its relationship with the values of a zero sum switching game is studied

global qualitative description of a class of nonlinear dynamical systems in this paper we propose a methodology to derive a qualitative description of the behavior of a system from an incompletely known nonlinear dynamical model the model is written as an algebraic structure with unknown parameters and or functions under some hypotheses we obtain a graph describing the possible transitions between regions defined by the trends of the state variables and their relative positions a qualitative simulation of the model can be compared with on line data for fault detection purpose we give the example of a nonlinear biological model in dimension three for the growth of cells in a bioreactor

generalized bsde with 2 reflecting barriers and stochastic quadratic growth abstract we study the existence of a solution for a one dimensional generalized backward stochastic differential equation with two reflecting barriers grbsde for short under assumptions on the input data which are weaker than that on the current literature in particular we construct a maximal solution for such a grbsde when the terminal condition is only f t measurable and the driver f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the variable z without assuming any p integrability conditions the work is suggested by the interest the results might have in dynkin game problem and american game option

distributions propres invariantes sur la paire symetrique gl 4 r gl 2 r gl 2 r abstract we study orbital integrals and invariant eigendistributions for the symmetric pair g h g l 4 r g l 2 r g l 2 r let q g h and let n be the set of nilpotents of q we first obtain an asymptotic behavior of orbital integrals around nonzero semisimple elements of q we study eigendistributions around such elements and give an explicit basis of eigendistributions on q n given by a locally integrable function on q n

approximate controllability of backward stochastic evolution equations in hilbert spaces in this paper we examine the approximate controllability of a semilinear backward stochastic evolution equations in hilbert spaces with non lipschitz coefficient

mean field backward stochastic differential equations in general probability spaces abstract in this paper we deal with a class of mean field backward stochastic differential equations in continuous time with an arbitrary filtered probability space we prove the existence and uniqueness of a solution for those equations with strengthened lipschitz assumption a comparison theorem is also established

integrales orbitales tordues sur les groupes de lie reductifs reels resume in this article we study orbital integrals on non connected real reductive groups we obtain a characterisation of these functions we construct a family of invariant eigendistributions and we use it to prove an invariant paley wiener theorem

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

zero sum stochastic differential games and backward equations abstract in this paper we are concerned with the applications to stochastic zero sum differential games of the results on backward stochastic differential equations using these techniques the existence of a saddle point in the bounded case is obtained if the isaacs condition holds furthermore this technique is also a very simple approach for the existence of an optimal strategy in the case of controlled diffusions

stochastic pdies and backward doubly stochastic differential equations driven by levy processes in this paper a new class of backward doubly stochastic differential equations driven by teugels martingales associated with a levy process satisfying some moment condition and an independent brownian motion is investigated we obtain the existence and uniqueness of solutions to these equations a probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given

anticipated backward stochastic differential equations driven by the teugels martingales abstract in this paper a class of anticipated backward stochastic differential equations driven by teugels martingales associated with levy process is investigated we obtain the existence and uniqueness of solutions to these equations by means of the fixed point theorem we show that a comparison theorem for this type of absdes also holds under some slight stronger conditions

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

two player nonzero sum stopping games in discrete time we prove that every two player non zero sum stopping game in discrete time admits an equilibrium in randomized strategies for every 0 we use a stochastic variation of ramsey theorem which enables us to reduce the problem to that of studying properties of equilibria in a simple class of stochastic games with finite state space

on solutions to backward stochastic partial differential equations for levy processes in this paper we prove the existence and uniqueness of the solution for a class of backward stochastic partial differential equations bspdes for short driven by the teugels martingales associated with a levy process satisfying some moment conditions and by an independent brownian motion an example is given to illustrate the theory

optimal play in a stochastic differential game this paper considers play in a two person zero sum differential game where the dynamics are given by a differential equation with additive white noise feedback strategies are employed standard results from control theory show that the maximizing player has an optimal response to any pre announced strategy of the minimizing player here it is shown that the minimizing player can achieve the upper value of the game by playing a strategy which is constructed by performing a pointwise min max on a certain fixed hamiltonian function

anticipated backward doubly stochastic differential equations in this paper we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations anticipated bdsdes the coefficients of these bdsdes depend on the future value of the solution y z we obtain the existence and uniqueness theorem and a comparison theorem for the solutions of these equations besides as an application we also establish a duality between the anticipated bdsdes and the delayed doubly stochastic differential equations delayed dsdes

necessary conditions for optimal control of stochastic systems with random jumps a maximum principle is proved for optimal controls of stochastic systems with random jumps the control is allowed to enter into both diffusion and jump terms the form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system the word pure here means the absence of the jump term in calculating the first order coefficient for the cost variation only a property for lebesgue integrals of scalar valued functions in the real number space cal r is used this shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned

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

stochastic viscosity solutions for spdes with continuous coefficients abstract in this note nonlinear stochastic partial differential equations spdes with continuous coefficients are studied via the solutions of backward doubly stochastic differential equations bdsdes with continuous coefficients we provide an existence result of stochastic viscosity sub and super solutions to this class of spdes under some stronger conditions we prove the existence of stochastic viscosity solutions

viability of moving sets for a nonlinear neumann problem abstract we prove that there exists a viscosity solution of a nonlinear neumann problem u i t x t a t u i t x f i t x u t x t x x u i t x 0 0 t t x d i 1 n u i t x n x g i t x u t x 0 t t x b d d i 1 n u t x h x x d which stays under some sufficient conditions in a prescribed set of time space dependent constraints k t x t x 0 t d the result is obtained by a stochastic approach we study the viability of the moving set k t x for a backward stochastic differential equation and we apply the feynman kac representation formula

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

backward stochastic differential equations with reflection and dynkin games we establish existence and uniqueness results for adapted solutions of backward stochastic differential equations bsde s with two reflecting barriers generalizing the work of el karoui kapoudjian pardoux peng and quenez existence is proved first by solving a related pair of coupled optimal stopping problems and then under different conditions via a penalization method it is also shown that the solution coincides with the value of a certain dynkin game a stochastic game of optimal stopping moreover the connection with the backward sde enables us to provide a pathwise deterministic approach to the game

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

formule d inversion des integrales orbitales tordues sur les groupes de lie reductifs reels resume we continue our study of twisted orbital integrals on real reductive groups in this paper we obtain an inversion formula in the spirit of bouaziz formula for the nontwisted case the distributions given by twisted orbital integrals are decomposed in terms of twisted characters of tempered representations

semisimple orbital integrals on the symplectic space for a real reductive dual pair we prove a weyl harish chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space w as an intermediate step we introduce a notion of a cartan subspace and a notion of an almost semisimple element in the symplectic space w we prove that the almost semisimple elements are dense in w finally we provide estimates for the orbital integrals associated with the different cartan subspaces in w

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

causality in device behavior abstract this paper shows how formal characterizations of causality and of the method of comparative statics long used in econometrics thermodynamics and other domains can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de kleer and brown 2 the formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system the intuitive concepts of causality captured by de kleer and brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations

a dynamic systems perspective on qualitative simulation abstract this paper presents a simple geometric interpretation of qualitative simulation qs based on the phase space representation of dynamic systems theory qs consists of two steps transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its long term behavior i recast transition analysis as a search problem in phase space and replace the assorted transition rules with two algebraic conditions the first condition determines transitions between arbitrarily shaped regions in phase space as opposed to qs which only handles n dimensional rectangles it also provides more accurate results by considering only the boundaries between regions the second condition determines whether nearby trajectories approach a fixed point asymptotically it obtains better results than qs by exploiting local stability properties i recast global interpretation of dissipative systems as a search for attractors in phase space and present a global interpretation strategy for the subset of these systems whose local behavior determines global behavior uniquely although limited in scope this strategy handles many systems that appear in the qs literature

dynkin game of stochastic differential equations with random coefficients and associated backward stochastic partial differential variational inequality a dynkin game is considered for stochastic differential equations with random coefficients we first apply qiu and tang s maximum principle for backward stochastic partial differential equations to generalize a krylov estimate for the distribution of a markov process to that of a non markov process and establish a generalized ito kunita wentzell formula which allows the test function as an ito process to take values in a sobolev space we then prove the verification theorem that the nash equilibrium point and the value of the dynkin game are characterized by the strong solution of the associated hamilton jacobi bellman isaacs equation which is currently a backward stochastic partial differential variational inequality bspdvi with two obstacles finally we prove the existence and uniqueness result and a comparison theorem for strong solution of the bspdvi

bsdes with two reflecting barriers the general result in this paper we show the existence of a solution for the bsde with two reflecting barriers when those latter are completely separated neither mokobodzki s condition nor the regularity of the barriers are supposed the main tool is the notion of local solution of reflected bsdes applications related to dynkin games and double obstacle variational inequality are given

controllability and the nature of quasi frequencies abstract using methods of dynamical systems we construct an example of a time dependent linear control process with quasi periodic coefficients for which the controllability properties of the system are very sensitive to the diophantine properties of the quasi frequencies

automatic analysis of one parameter planar ordinary differential equations by intelligent numeric simulation abstract this paper describes research on automating the analysis of physical systems modeled by ordinary differential equations it describes a program called poincare that analyzes one parameter autonomous planar systems at the level of experts through a combination of theoretical dynamics numerical simulation and geometric reasoning the input is the system a bounding box for the system state a bounding interval for the parameter and error tolerances poincare partitions the parameter interval into open subintervals of equivalent behavior bounded by bifurcation points classifies the bifurcation points and constructs representative phase diagrams for the subintervals it detects local and global generic one parameter bifurcations it constructs the phase diagrams by identifying fixed points saddle manifolds and limit cycles and partitioning the remaining trajectories into open regions of uniform asymptotic behavior it obtains the region boundaries by numeric simulation guided by theoretical knowledge it determines the behavior near fixed points from the jacobian of the system scans outward to find basins of attractors and limit cycles and stops at the bounding box

a generalized harish chandra method of descent for reductive lie algebras abstract let g be a connected real reductive group and m a connected reductive subgroup of g with lie algebras g and m respectively we assume that g and m have the same rank we define a map from the space of orbital integrals of m into the space of orbital integrals of g which we call a transfer we then consider the transpose of the transfer this can be viewed as a map from the space of g invariant distributions of g to the space of m invariant distributions of m and can be considered as a restriction map from g to m we prove that this map extends harish chandra method of descent and we obtain a generalization of the radial component theorem we give an application

on the starting and stopping problem application in reversible investments in this work we solve completely the starting and stopping problem when the dynamics of the system are a general adapted stochastic process we use backward stochastic differential equations bsdes and snell envelopes finally we give some numerical results

an example of almost universally observable vector fields on p 1 r abstract using methods of dynamical systems we construct examples of smooth almost universally observable vector fields on the projective 1 space these vector fields are non linear non autonomous and their time dependence is almost periodic

dynkin game of convertible bonds and their optimal strategy abstract this paper studies the valuation and optimal strategy of convertible bonds as a dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method we first reduce such a dynkin game to an optimal stopping time problem with state constraint and then in a markovian setting we investigate the optimal strategy by analyzing the properties of the corresponding free boundary including its position asymptotics monotonicity and regularity we identify situations when call precedes conversion and vice versa moreover we show that the irregular payoff results in the possibly non monotonic conversion boundary surprisingly the price of the convertible bond is not necessarily monotonic in time it may even increase when time approaches maturity

automatic qualitative analysis of dynamic systems using piecewise linear approximations abstract this paper explores automating the qualitative analysis of physical systems it describes a program called plr for piecewise linear reasoner that formalizes an analysis strategy employed by experts plr takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values it approximates intractable nonlinear systems with piecewise linear ones analyzes the approximations and draws conclusions about the original systems it chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes yet simple enough to be analyzed completely and efficiently it derives additional properties such as boundedness or periodicity by theoretical methods plr s analysis depends on abstract properties of systems rather than on specific numeric values this makes its conclusions more robust and enables it to handle parameterized equations transparently i demonstrate plr on several common nonlinear systems and on published examples from mechanical engineering

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

reflected scheme for doubly reflected bsdes with jumps and rcll obstacles we introduce a discrete time reflected scheme to solve doubly reflected backward stochastic differential equations with jumps in short drbsdes driven by a brownian motion and an independent compensated poisson process as in dumitrescu and labart 2014 we approximate the brownian motion and the poisson process by two random walks but contrary to this paper we discretize directly the drbsde without using a penalization step this gives us a fully implementable scheme which only depends on one parameter of approximation the number of time steps n contrary to the scheme proposed in dumitrescu and labart 2014 which also depends on the penalization parameter we prove the convergence of the scheme and give some numerical examples

on the quasi linear reflected backward stochastic partial differential equations abstract this paper is concerned with the quasi linear reflected backward stochastic partial differential equation rbspde for short basing on the theory of backward stochastic partial differential equation and the parabolic capacity and potential we first associate rbspde to a variational problem and via the penalization method we prove the existence and uniqueness of the solution for linear rbspde with laplacian leading coefficients with the continuity approach we further obtain the well posedness of general quasi linear rbspdes related results including ito formulas for backward stochastic partial differential equations with stochastic regular measures the comparison principle for solutions of rbspdes and the connections with reflected backward stochastic differential equations and optimal stopping problems are addressed as well

stochastic pdies with nonlinear neumann boundary conditions and generalized backward doubly stochastic differential equations driven by levy processes in this paper a new class of generalized backward doubly stochastic differential equations gbdsdes in short driven by teugels martingales associated with levy process and the integral with respect to an adapted continuous increasing process is investigated we obtain the existence and uniqueness of solutions to these equations a probabilistic interpretation for solutions to a class of stochastic partial differential integral equations pdies in short with a nonlinear neumann boundary condition is given

anticipated backward stochastic differential equations in this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations anticipated bsdes in these equations the generator includes not only the values of solutions of the present but also the future we show that these anticipated bsdes have unique solutions a comparison theorem for their solutions and a duality between them and stochastic differential delay equations

numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers in this paper we study different algorithms for reflected backward stochastic differential equations bsde in short with two continuous barriers based on the framework of using a binomial tree to simulate 1 d brownian motion we introduce numerical algorithms by the penalization method and the reflected method respectively in the end simulation results are also presented

continuous time dynkin games with mixed strategies let x y z be a triple of payoff processes defining a dynkin game tilde r sigma tau e left x sigma 1 tau sigma y tau 1 tau sigma z tau 1 tau sigma right where sigma and tau are stopping times valued in 0 t in the case z y it is well known that the condition x leq y is needed in order to establish the existence of value for the game i e inf tau sup sigma tilde r sigma tau sup sigma inf tau tilde r sigma tau in order to remove the condition x leq y we introduce an extension of the dynkin game by allowing for an extended set of strategies namely the set of mixed strategies the main result of the paper is that the extended dynkin game has a value when z leq y and the processes x and y are restricted to be semimartingales continuous at the terminal time t

invariant distributions supported on the nilpotent cone of a semisimple lie algebra let g be a semisimple complex lie algebra with adjoint group g and 1 g be the algebra of differential operators with polynomial coefficients on g if go is a real form of g we give the decomposition of the semisimple 1 g g module of invariant distributions on go supported on the nilpotent cone

bounded variation singular stochastic control and dynkin game we consider a bounded variation singular stochastic control problem with value v in a general situation with control of a diffusion and nonlinear cost functional defined as solution to a backward stochastic differential equation bsde associated with this is a dynkin game with value u we establish the well known relation frac partial partial x v u for this general situation a saddle point for the dynkin game is given by the pair of first action times of an optimal control the methods are from stochastic analysis and include a priori estimates pathwise construction and comparison theorems for forward stochastic differential equations fsde and bsde

on covariant functions and distributions under the action of a compact group abstract let g be a compact subgroup of gl n r acting linearly on a finite dimensional complex vector space e b malgrange has shown that the space c r n e g of c and g covariant functions is a finite module over the ring c r n g of c and g invariant functions first we generalize this result for the schwartz space s r n e g of g covariant functions secondly we prove that any g covariant distribution can be decomposed into a sum of g invariant distributions multiplied with a fixed family of g covariant polynomials this gives a generalization of an oksak result proved in 4

second order backward stochastic differential equations and fully nonlinear parabolic pdes for a d dimensional diffusion of the form dxt xt dt xt dwt and continuous functions f and g we study the existence and uniqueness of adapted processes y z and a solving the second order backward stochastic differential equation 2bsde dyt f t xt yt zt t dt z dxt t 0 t dzt at dt t dxt

the l2 lefschetz numbers of hecke operators introduction 5 1 hecke operators and l2 cohomology 52 the spectral decomposition of cohomology 6 3 application of the trace formula 54 the functions pa t 5 5 proof of theorem 5 1 6 the main formula appendix bibliography

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