Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise

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

Two-dimensional Stochastic Navier-stokes Equations with Fractional Brownian Noise

We study the perturbation of the two-dimensional stochastic Navier-Stokes equation by a Hilbert-space-valued fractional Brownian noise. Each Hilbert component is a scalar fractional Brownian noise in time, with a common Hurst parameter H and a specific intensity. Because the noise is additive, simple Wiener-type integrals are suffi cient for properly defining the problem. It is resolved by sepa...

Existence of strong solutions and uniqueness in law for stochastic differential equations driven by fractional Brownian motion

In this paper we establish the existence of path-wise solutions and the uniqueness in law for multidimensional stochastic differential equations driven by a multi-dimensional fractional Brownian motion with Hurst parameter H > 12 .

A Note on Strong Solutions of Stochastic Differential Equations with a Discontinuous Drift Coefficient

The existence of a mean-square continuous strong solution is established for vectorvalued Itô stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion coefficient. A scalar stochastic differential equation with the Heaviside function as its drift coefficient is considered as an example. Upper and lower s...

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion