Stochastic Linear-Quadratic Control with State Dependent Fractional Brownian Noise and Stochastic Coefficients

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Linear-quadratic Control for Stochastic Equations in a Hilbert Space with Fractional Brownian Motions

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...

on time-dependent neutral stochastic evolution equations with a fractional brownian motion and infinite delays

in this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional brownian motion in a hilbert space. we establish the existence and uniqueness of mild solutions for these equations under non-lipschitz conditions with lipschitz conditions being considered as a special case. an example is provided to illustrate the theory

Stochastic H2/H∞ control with state-dependent noise

For a system governed by Itô-type nonlinear stochastic differential equation with state-dependent noise, the H2/H∞ control problem is considered, which combines the H2 optimization with the robust H∞ performance. A cross-coupled Hamilton-Jacobi equations associated with the nonlinear stochastic H2/H∞ control are obtained, based on which, sufficient conditions for designing the finite and infini...