Parameter estimation of stochastic differential equation driven by small fractional noise

Stochastic Heat Equation Driven by Fractional Noise and Local Time

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...

Parameter Estimation of Stochastic Differential Equation

Non-parametric modeling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochasti...

A singular stochastic differential equation driven by fractional Brownian motion∗

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H > 1 2 . Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t > 0.

A quasilinear stochastic partial differential equation driven by fractional white noise

We approximate the solution of a quasilinear stochastic partial differential equation driven by fractional Brownian motion BH(t); H ∈ (0, 1), which was calculated via fractional White Noise calculus, see [5].

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