An Approximate Martingale Convergence Theorem on Locally Compact Abelian Groups

Michael S. Bingham
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Michael S. Bingham: The University, Department of Statistics

A chapter in Probability Measures on Groups X, 1991, pp 11-17 from Springer

Abstract: Summary The purpose of this paper is to present an analogue for some group—valued stochastic processes of the classical martingale convergence theorem for real—valued processes. For group—valued processes the usual concepts of expectation and martingale are generally without meaning and so must be replaced by suitable alternatives. In particular, the martingale condition is replaced by an “approximate martingale condition” similar to the one introduced in Bingham (1986).

Keywords: Compact Abelian Group; Local Martingale; Positive Definite Function; Compact Open Topology; Usual Concept (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2364-6_2

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DOI: 10.1007/978-1-4899-2364-6_2

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