Related papers: Stochastic Variational Inequalities on Non-Convex …
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…
This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a…
Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ \xi\sigma (u_t(x)) \dot F(t,x), \end{equation*} where $\xi$ is a positive parameter and $\sigma$ is a globally…
This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…
In this article we prove the continuity of the deterministic function $u:[0,T]\times \mathcal{\bar{D}}\rightarrow \mathbb{R}$, defined by $u(t,x):=Y_{t}^{t,x}$, where the process $(Y_{s}^{t,x})_{s\in[t,T]}$ is given by the generalized…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
This paper establishes results on the existence and uniqueness of solutions to McKean-Vlasov equations, also called mean-field stochastic differential equations, in an infinite-dimensional Hilbert space setting with irregular drift. Here,…
As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds…
We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing…
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
For $q \in (0, \infty)$, we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big( D_\xi f(x,u,Du) \big) = - D_u f(x,u,Du) \end{align*} in a…
In this paper, we mainly focus on the set-valued (stochastic) analysis on the space of convex, closed, but possibly unbounded sets, and try to establish a useful theoretical framework for studying the set-valued stochastic differential…
In this note we consider a class of neutral stochastic functional differential equations with finite delay driven simultaneously by a fractional Brownian motion and a Poisson point processes in a Hilbert space. We prove an existence and…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
We consider the class of non-linear stochastic partial differential equations studied in \cite{conusdalang}. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are…
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…
This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than processes in the generalized sense. We consider a first order…