Equivalent Stochastic Systems

[+] Author and Article Information
Y. K. Lin, G. Q. Cai

Center for Applied Stochastics Research, Florida Atlantic University, Boca Raton, FL 33431

J. Appl. Mech 55(4), 918-922 (Dec 01, 1988) (5 pages) doi:10.1115/1.3173742 History: Received September 24, 1987; Revised February 25, 1988; Online July 21, 2009


Equivalent stochastic systems are defined as randomly excited dynamical systems whose response vectors in the state space share the same probability distribution. In this paper, the random excitations are restricted to Gaussian white noises; thus, the system responses are Markov vectors, and their probability densities are governed by the associated Fokker-Planck equations. When the associated Fokker-Planck equations are identical, the equivalent stochastic systems must share both the stationary probability distribution and the transient nonstationary probability distribution under identical initial conditions. Such systems are said to be stochastically equivalent in the strict (or strong) sense. A wider class, referred to as the class of equivalent stochastic systems in the wide (or weak) sense, also includes those sharing only the stationary probability distribution but having different Fokker-Planck equations. Given a stochastic system with a known probability distribution, procedures are developed to identify and construct equivalent stochastic systems, both in the strict and in the wide sense.

Copyright © 1988 by ASME
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