Stochastic Relations of Random Variables and Processes

Lasse Leskelä ()
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Lasse Leskelä: Helsinki University of Technology

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 523-546

Abstract: Abstract This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the order relation. The main contributions of the paper are: a functional characterization of stochastic relations, necessary and sufficient conditions for the preservation of stochastic relations, and an algorithm for finding subrelations preserved by probability kernels. The theory is illustrated with applications to hidden Markov processes, population processes, and queueing systems.

Keywords: Stochastic order; Stochastic relation; Subrelation; Coupling; Probability kernel; Random dynamical system; Markov process; 60B99; 60E15; 60G99; 60J99 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0216-8

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