An existence theorem for linear stochastic differential equations

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

The Stable Manifold Theorem for Semi-linear Stochastic Evolution Equations and Stochastic Partial Differential Equations I: the Stochastic Semiflow

The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts I, II. In Part I (this pap...

A Unified Existence and Uniqueness Theorem for Stochastic Evolution Equations

An existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise. 2000 Mathematics subject classification: primary 60H15; secondary 35K90.

Existence and Uniqueness Theorem for Stochastic Differential Equations with Self-Exciting Switching

Algorithms for Linear Stochastic Delay Differential Equations

Models consisting of linear, N-dimensional stochastic delay differential equations present a particular set of challenges for numerical simulation. While the user often seeks the probability density function of the solution, currently available methods rely on Monte Carlo sampling to generate sample paths, from which a density function must be estimated statistically. In the present work, we de...