相关论文: Unique Continuation for Stochastic Parabolic Equat…

This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…

We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further boundary condition. We treat two different cases: (i) uniform…

The aim of the book is to present some recent results in the theory of stochastic It\^o equations with singular deterministic part (drift) and its applications to second-order elliptic and parabolic equations with singular first-order…

The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the…

We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution.…

We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…

Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…

We establish the strong unique continuation property of fractional orders of linear elliptic equations with Lipschitz coefficients by establishing monotonicity of some Almgren-type frequency functional via an extension procedure.

We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.

The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns…

We develop a new generalized coupling approach to the study of stochastic delay equations with H\"older continuous coefficients, for which analytical PDE-based methods are not available. We prove that such equations possess unique weak…

This paper is concerned with the null controllability for linear backward stochastic parabolic equations with dynamic boundary conditions and convection terms. Using the classical duality argument, the null controllability is obtained via…

Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic…

We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type…

This paper studies the regularity of weak solutions to a class of parabolic perturbed fractional $1$-Laplace equations. Our analysis combines finite difference quotients, energy estimates, and iterative arguments, with a key step being the…