Related papers: An operatorial approach to stochastic partial diff…

We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…

We investigate spaceability phenomena in linear dynamics from a structural perspective. Given a continuous linear operator \(T:X \to X\), we introduce the set \(\Omega(T)\), consisting of all continuous linear operators \(h:X \to X\) for…

We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…

The stochastic differential equation $\dot{x}(t) = ax(t) + bx(t-\tau) + c x(t) \xi(t)$ with a time-delayed feedback and a multiplicative Gaussian noise is shown to be related to Kardar-Parisi-Zhang universality class of growing surfaces.

We study time-fractional stochastic Navier-Stokes equations on a bounded domain of $\R^2$ (the restriction to dimension two is essential for the bilinear estimates via Sobolev embeddings) driven by a Hermite process $Z_H^k$ of order $k\ge1$…

In this article, we consider the following class of stochastic partial differential equations (SPDE): \begin{equation*} \left\{\begin{aligned}\mathrm{d} \mathbf{X}(t)&=\mathrm{A}(t,\mathbf{X}(t))\mathrm{d}…

In this paper we focus on the stochastic Euler-Poincar\'{e} equations with pseudo-differential/multiplicative noise. We first establish two new cancellation properties on pseudo-differential operators, which play a key role in energy…

We present an innovating sensitivity analysis for stochastic differential equations: We study the sensitivity, when the Hurst parameter~$H$ of the driving fractional Brownian motion tends to the pure Brownian value, of probability…

We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…

We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…

This paper proposes and analyzes a novel fully discrete finite element scheme with the interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-side Lipschitz condition and…

This article studies the Stochastic Degasperis-Procesi (SDP) equation on $\mathbb{R}$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $L^2(\mathbb{R})\cap L^{2+\delta}(\mathbb{R})$, for…

We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In opposition to the popular approach with projection methods,…

We consider a mixed stochastic differential equation $d{X_t}=a(t,X_t)d{t}+b(t,X_t) d{W_t}+c(t,X_t)d{B^H_t}$ driven by independent multidimensional Wiener process and fractional Brownian motion. Under Hormander type conditions we show that…

We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and…

We prove existence of martingale solutions for the stochastic Cahn-Hilliard equation with degenerate mobility and multiplicative Wiener noise. The potential is allowed to be of logarithmic or double-obstacle type. By extending to the…

Motivated by applications to probability and mathematical finance, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable…

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is…

We consider an abstract mixed variational problem governed by a nonlinear operator $A$ and a bifunctional $J$, in a real reflexive Banach space $X$. The operator $A$ is assumed to be continuous, Lipschitz continuous on each bounded subset…