相关论文: Stochastic PDEs involving a bilaplacian operator

Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…

Controlling the monotonicity and growth of Leray--Lions' operators including the $p$-Laplacian plays a fundamental role in the theory of existence and regularity of solutions to second order nonlinear PDE. We collect, correct, and supply…

We consider positive singular solutions of PDEs arising from double phase functionals. Exploiting a rather new version of the moving plane method originally developed by Sciunzi, we prove symmetry and monotonicity properties of such…

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong…

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is…

The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the existence…

The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus…

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We assume that the nonlinear term is merely monotone…

In this paper, we prove a convergence theorem for singular perturbations problems for a class of fully nonlinear parabolic partial differential equations with ergodic structures. The limit function is represented as the viscosity solution…

In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises \bess…

In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operators whose symbols depend only on time and spatial frequencies.…

This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of…

In this work, the synchronization problem of a master-slave system of autonomous ordinary differential equations (ODEs) is considered. Here, the systems are, chaotic with a nonlinearity represented by a piecewise linear function,…

In our pursuit of finding a zero for a monotone and Lipschitz continuous operator $M : \R^n \rightarrow \R^n$ amidst noisy evaluations, we explore an associated differential equation within a stochastic framework, incorporating a correction…

In this paper, we study the existence of random periodic solutions for nonlinear stochastic differential equations with additive white noise. We extend the input-to-state characteristic operator of the system to the non-autonomous…

In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…

We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show…

We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss non-autonomous partial differential equations with an abstract realization of the stochastic integral on the right-hand side. Our…

Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete…

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…