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).
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References
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Bingham, M.S. (1991). An Approximate Martingale Convergence Theorem on Locally Compact Abelian Groups. In: Heyer, H. (eds) Probability Measures on Groups X. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2364-6_2
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DOI: https://doi.org/10.1007/978-1-4899-2364-6_2
Publisher Name: Springer, Boston, MA
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