Stochastic Volterra equations in Banach spaces and stochastic partial differential equation

Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations*

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique max...

Stochastic Volterra Differential Equations in Weighted Spaces

In the following paper, we provide a stochastic analogue to work of Shea and Wainger by showing that when the measure and state-independent diffusion coefficient of a linear Itô–Volterra equation are in appropriate Lp– weighted spaces, the solution lies in a weighted Lp–space in both an almost sure and moment sense.

Stochastic Partial Differential Equations

Stochastic Partial Differential Equations and Submanifolds in Hilbert Spaces

The goal of this appendix is to provide results about stochastic partial differential equations driven by Wiener processes and Poisson measures and results about submanifolds in Hilbert spaces. It should serve as a reference for auxiliary results that we require in [7].

Stationary Solutions of Stochastic Differential Equation with Memory and Stochastic Partial Differential Equations

We explore Itô stochastic differential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proved if the dependence on the past decays sufficiently fast. The results of this paper ar...