A probabilistic theory of random maps
type: Item
instance of: scholarly article
title: A probabilistic theory of random maps
zbMATH Open document ID: 1072.60060
author: Niranjan Chakravarthy
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2005-05-12T00:00:00Z
review text: The forward and backward Kolomogorov equations and the Fokker-Planck equation, resp., characterize transition probabilities and invariant measures, resp., for Markov semigroups with continuous time. Often they are invoked for the investigation of stochastic differential equations. The paper suggests an analogue of the forward and backward Kolmogorov equations and of the Fokker-Planck equation for certain classes of random maps, defining discrete time Markov chains. For this purpose, equations satisfied by transition probabilities are expanded in Taylor series. Numerically obtained results illustrate the quantities for certain one- and two-dimensional maps. For earlier work in this context see also \textit{R. F. Pawula} [IEEE Trans. Inf. Theory 13, 33--41 (1967; Zbl 0154.42401)].
reviewed by: Hans Crauel
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 2167737
zbMATH Keywords: discrete time stochastic systems
zbMATH Keywords: Kolmogorov equation
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: Pawula theorem
MaRDI profile type: Publication
full work available at URL: j.cnsns.2004.03.004
OpenAlex ID: W2079963622
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DOI: 10.1016/J.CNSNS.2004.03.004
description: scientific article; zbMATH DE number 2167737