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Doob's inequalities revisited: A maximal H1-embedding

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  • Jacka, S. D.

Abstract

An embedding of an arbitrary centred law [mu] in a Brownian motion (that is a stopping time T and a Brownian motion B such that (Bt)=[mu] and (Bt[Lambda]T; t[greater-or-equal, slanted]0) is found such that B*T has a law which dominates that of M*[tau], where the pair (M, [tau]) is any other ui embedding of [mu] in a martingale.

Suggested Citation

  • Jacka, S. D., 1988. "Doob's inequalities revisited: A maximal H1-embedding," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 281-290, September.
    • Handle: RePEc:eee:spapps:v:29:y:1988:i:2:p:281-290
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    Cited by:

    1. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.
    2. Graversen, S. E. & Peskir, G., 1997. "On Doob's maximal inequality for Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 111-125, July.
    3. Cox, Alexander M.G. & Obłój, Jan, 2015. "On joint distributions of the maximum, minimum and terminal value of a continuous uniformly integrable martingale," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3280-3300.

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