Related papers: The obstacle problem for semilinear parabolic part…

Using probabilistic methods, we establish a-priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity which has quadratic growth in the…

Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217,…

Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…

This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in…

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces allowing the derivatives of the…

The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized…

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…

We consider a two obstacle problem for the parabolic biharmonic equation in a bounded domain. We prove long time existence of solutions via an implicit time discretization scheme, and we investigate the regularity properties of solutions.

In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general…

In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new…

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…

We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in…

We study linear backward stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the terminal time is replaced by a condition that holds almost surely and mixes…

This paper, is an attempt to extend the notion of stochastic viscosity solution to reflected semi-linear stochastic partial differential equations (RSPDEs, in short) with non-Lipschitz condition on the coefficients. Our method is fully…

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used…

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.…

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator $f$ has quadratic growth in the $z$-variable. In…

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate…

The Feynman-Kac formulae (FKF) express local solutions of partial differential equations (PDEs) as expectations with respect to some complementary stochastic differential equation (SDE). Repeatedly sampling paths from the complementary SDE…

Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional…