Han X., Kloeden P.E. Random Ordinary Differential Equations and Their Numerical Solution

Springer Nature Singapore Pte Ltd., 2017. — 252 p. — (Probability Theory and Stochastic Modelling 85) — ISBN: 9811062641.This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).Random and Stochastic Ordinary Differential EquationsRandom Ordinary Differential Equations
Stochastic Differential Equations
Random Dynamical Systems
Numerical Dynamics
Taylor Expansions
Taylor Expansions for Ordinary and Stochastic Differential Equations
Taylor Expansions for RODEs with Affine Noise
Taylor-Like Expansions for General Random Ordinary Differential Equations
Numerical Schemes for Random Ordinary Differential Equations
Numerical Methods for Ordinary and Stochastic Differential Equations
Itô–Taylor Schemes for RODEs with Itô Noise
Numerical Schemes for RODEs with Affine Noise
RODE-Taylor Schemes: General Case
Numerical Stability
Stochastic Integrals: Simulation and Approximation
Random Ordinary Differential Equations in the Life Sciences
Comparative Simulations of Biological Systems
Chemostat
Immune System Virus Model
Random Markov Chains
Appendixes
Probability Spaces
Chain Rule for Affine RODEs
Covariance Matrix of a Fractional Brownian Motion and Its Integral