Related papers: Stochastic Integral Equations for Walsh Semimartin…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
Shift Harnack and integration by part formula are establish for semilinear spde with delay and a class of stochastic semilinear evolution equation which cover the hyperdissipative Naiver-Stokes/Burges equation. For the case of stochastic…
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can…
We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of Fontbona-Gu\'erin-M\'el\'eard, we propose a…
We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the…
In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an It^o stochastic integral \int H(X)dM, where H(x) is some particular measurable choice of…
We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a…
In this paper we consider the three-dimensional compressible MHD system with stochastic external forces in a bounded domain. We obtain the existence of martingale solution which is a weak solution for the fluid variables, the Brownian…
In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…
We consider a stochastic nonlinear Schr\"odinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing stochastic NLS in $H^1$ on compact manifolds and bounded domains. We construct a…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii)…
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 examine the numerical approximation of a quasilinear stochastic differential equation (SDE) with multiplicative fractional Brownian motion. The stochastic integral is interpreted in the Wick-It\^o-Skorohod (WIS) sense that is well…
The numerical analysis of stochastic parabolic partial differential equations of the form $$ du + A(u) = f \,dt + g \, dW, $$ is surveyed, where $A$ is a partial operator and $W$ a Brownian motion. This manuscript unifies much of the theory…
We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…
Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of…