Related papers: A converse comparison theorem for backward stochas…
We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for…
In this paper we obtain a Wong-Zakai approximation to solutions of backward doubly stochastic differential equations.
The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…
We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…
An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure…
In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence…
We study the problem of approximation of solutions of the Skorokhod problem and reflecting stochastic differential equations (SDEs) with jumps by sequences of solutions of equations with penalization terms. Applications to discrete…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness…
Anticipated backward stochastic differential equation (ABSDE) studied the first time in 2007 is a new type of stochastic differential equations. In this paper, we establish a general comparison theorem for 1-dimensional ABSDEs with the…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
In this paper we consider the maximum principle of optimal control for a stochastic control problem. This problem is governed by a system of fully coupled multi-dimensional forward-backward doubly stochastic differential equation with…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
In this note, we derive an existence and uniqueness results for delayed backward stochastic differential equation with only integrable data.
This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish $L^2$ stability and convergence of the difference approximations under conditions that are less strict than those required…
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are…