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- W2080246331 abstract "University of California, Berkeley A number of conditions for convergence of sub-martingales are known today. The earliest of these in Doob's theorem [2] which requires an upper bound on the expectations of x. . Snell [4] then generalized Doob's result by conditioning the expectations. Chow [1] proved a different generalization based on random times. It was suggested by Lobve that the two results could be combined to yield a further generalization. The theorem presented here is of this nature. The proof adheres very closely to Chow's approach. LEM1A. Let (xn , n _ 1, En) be a sub-martingale sequence. Then for all k, n, m, k < n ? m:" @default.
- W2080246331 created "2016-06-24" @default.
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- W2080246331 date "1964-12-01" @default.
- W2080246331 modified "2023-09-29" @default.
- W2080246331 title "A Note on Convergence of Sub-Martingales" @default.
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- W2080246331 doi "https://doi.org/10.1214/aoms/1177700404" @default.
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