相关论文: An elementary approach to Stochastic Differential …
The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an It\^{o} formula like the solution…
This is an overview of the basic tools of nonsmooth analysis which are grounded on nonstandard models of set theory. By way of illustration we give a criterion for an infinitesimally optimal path of a general discrete dynamic system.
Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…
In this paper, we study the existence and uniqueness of mild solution for a stochastic neutral partial functional integro-differential equation with delay in a Hilbert space driven by a fractional Brownian motion and with non-deterministic…
In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion (fBm) and a Wiener process and having jumps. We prove that this equation has a unique solution and show that all its moments are finite.
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
By the approximation method introduced in \cite{FYW}, the existence and uniqueness are proved for a class of distribution-dependent stochastic functional differential equations (DDSFDEs). Moreover, combining the Harnack and shift-Harnack…
In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while…
We propose a general strategy for solving nonlinear integro-differential evolution problems with periodic boundary conditions, where no direct maximum/minimum principle is available. This is motivated by the study of recent macroscopic…
In this paper, we study forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP in short). Both the probabilistic interpretation for the solutions to a class of quasilinear…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
Nonlinear stochastic motion presents significant challenges for Bayesian particle tracking. To address this challenge, this paper proposes a framework to construct an invertible transformation that maps the nonlinear state-space model (SSM)…
In this paper, we study the existence and uniqueness of a class of stochastic differential equations driven by fractional Brownian motions with arbitrary Hurst parameter $H\in (0,1)$. In particular, the stochastic integrals appearing in the…
We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…