Related papers: The Obstacle Problem for Quasilinear Stochastic In…
The aim of this paper is to study, in the infinite dimensional framework, the existence and uniqueness for the solution of the following multivalued generalized backward stochastic differential equation, considered on a random, possibly…
We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward…
In this paper we obtain a comparison theorem for backward stochastic partial differential equation (SPDEs) with jumps. We apply it to introduce space-dependent convex risk measures as a model for risk in large systems of interacting…
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…
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs) with infinite anticipation, where the generator depends on the entire future values of the solution in infinite horizon. We show that the new BSDEs…
We propose a new deep learning algorithm for solving high-dimensional parabolic integro-differential equations (PIDEs) and forward-backward stochastic differential equations with jumps (FBSDEJs). This novel algorithm can be viewed as an…
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…
This article deals with stochastic partial differential equations with quadratic nonlinearities perturbed by small additive and multiplicative noise. We present the approximate solution of the original equation via the amplitude equation…
We are concerned with a priori estimates for the obstacle problem of a wide class of fully nonlinear equations on Riemannian manifolds. We use new techniques introduced by Bo Guan and derive new results for a priori second order estimates…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
In this paper we obtain a Wong-Zakai approximation to solutions of backward doubly stochastic differential equations.
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…
The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the…
In this letter we study variational obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function…
In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the…