Related papers: A Numerical scheme for backward doubly stochastic …
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…
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration.…
We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…
In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, we obtain two approximation results, namely, a BSDE approximation and a numerical approximation. The BSDE…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
In this paper we present a unified approach to establish gradient type formulas and Bismut type formulas for backward stochastic differential equations (BSDEs). This approach relies on a mix of derivative formulas with respect to the…
This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…
We are investigating the first strong convergence analysis of a numerical method for stochastic differential algebraic equations (SDAEs) under a non-global Lipschitz setting. It is well known that the explicit Euler scheme fails to converge…
The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…
This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a…
For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well as the existence of a strongly convergent numerical method…
The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). This…
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…
Finite difference schemes in the spatial variable for degenerate stochastic parabolic PDEs are investigated. Sharp results on the rate of $L_p$ and almost sure convergence of the finite difference approximations are presented and results on…
The rates of strong convergence for various approximation schemes are investigated for a class of stochastic differential equations (SDEs) which involve a random time change given by an inverse subordinator. SDEs to be considered are unique…
We present a novel solution method for It\^o stochastic differential equations (SDEs). We subdivide the time interval into sub-intervals, then we use the quadratic polynomials for the approximation between two successive intervals. The main…
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. BSDEs in applications are often nonlinear and high-dimensional. In nearly all…