Stochastic Heat Equation Driven by Fractional Noise and Local Time

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

Feynman-Kac formula for heat equation driven by fractional white noise

In this paper we establish a version of the Feynman-Kac formula for the stochastic heat equation with a multiplicative fractional Brownian sheet. We prove the smoothness of the density of the solution, and the Hölder regularity in the space and time variables.

Feynman-Kac formula for fractional heat equation driven by fractional white noise

In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is ...

The Stochastic Heat Equation with a Fractional-colored Noise: Existence of the Solution

Abstract. In this article we consider the stochastic heat equation ut −∆u = Ḃ in (0, T )× R, with vanishing initial conditions, driven by a Gaussian noise Ḃ which is fractional in time, with Hurst index H ∈ (1/2, 1), and colored in space, with spatial covariance given by a function f . Our main result gives the necessary and sufficient condition on H for the existence of the process solution. W...