Linear Stochastic Systems: A White Noise Approach

A White Noise Approach to Stochastic Neumann Boundary Value Problems

We illustrate the use of white noise analysis in the solution of stochastic partial diierential equations by solving explicitly the stochastic Neumann boundary value problem LU(x) ? c(x)U(x) = 0; x 2 D R d ; (x) rU(x) = ?W(x); x 2 @D where L is a uniformly elliptic linear partial diierential operator and W (x), x 2 R d , is d-parameter white noise. 1. Introduction Since the seminal book by Hida...

White Noise Analysis of Coupled Linear-Nonlinear Systems

Abstract. We present an asymptotic analysis of two coupled linear-nonlinear systems. Through measuring first and second input-output statistics of the systems in response to white noise input, one can completely characterize the systems and their coupling. The proposed model is similar to a widely used phenomenological model of neurons in response to sensory stimulation and may be used to help ...

Stochastic Nonlinear Schrödinger Equations with Linear Multiplicative Noise: Rescaling Approach

We prove well-posedness results for stochastic nonlinear Schrödinger equations with linear multiplicative Wiener noise including the non-conservative case. Our approach is different from the standard literature on stochastic nonlinear Schrödinger equations. By a rescaling transformation we reduce the stochastic equation to a random nonlinear Schrödinger equation with lower order terms and treat...

Response statistics of linear stochastic systems: A simultaneous diagonalisation approach

Residual Generation in Linear Stochastic Systems - A Polynomial Approach

A polynomial design algorithm for innovation/residual generation for fault diagnosis is given. The class of systems considered is linear stochastic state-space and descriptor systems in both continuous and discrete time. A new class of residual generators based on stochastic models is defined and design algorithms are derived. The algorithms is based on standard operations such as null-space co...