Related papers: The time fractional stochastic partial differentia…
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and fractional Laplacians. We first establish maximum principles…
In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by H\"older continuous functions of order $H>\frac12$. As an application, we consider stochastic differential…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a $C_0-$semigroup and one linear bounded operator with Wick-type multiplication, all of them set…
We study existence and uniqueness of solutions to the equation $dX_t=b(X_t)dt + dB_t$, where $b$ is a distribution in some Besov space and $B$ is a fractional Brownian motion with Hurst parameter $H\leqslant 1/2$. First, the equation is…
In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation…
We consider a stochastic Camassa-Holm equation driven by a one-dimensional Wiener process with a first order differential operator as diffusion coefficient. We prove the existence and uniqueness of local strong solutions of this equation.…
In the present work, we investigate stochastic third grade fluids equations in a $d$-dimensional setting, for $d = 2, 3$. More precisely, on a bounded and simply connected domain $\mathcal{D}$ of $\mathbb{R}^d$, $d = 2,3$, with a…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
This paper develops an $\alpha$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed L\'evy noise (TCSDEwLNs) with time-space-dependent…
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the…
We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
In this article, we study the regularity of solutions to inhomogeneous time-fractional evolution equations involving anisotropic non-local operators in mixed-norm Sobolev spaces of variable order, with non-trivial initial conditions. The…
In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schr\"{o}dinger equation, with either focusing or defocusing nonlinearity, driven by nonlinear multiplicative L\'evy noise in the Marcus…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of L\'evy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D…
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}…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…