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A Generalization of the Submartingale Property: Maximal Inequality and Applications to Various Stochastic Processes

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  • János Engländer

    (University of Colorado)

Abstract

We generalize the notion of the submartingale property and Doob’s inequality. Furthermore, we show how the latter leads to new inequalities for several stochastic processes: certain time series, Lévy processes, random walks, processes with independent increments, branching processes and continuous state branching processes, branching diffusions and superdiffusions, as well as some Markov processes, including geometric Brownian motion.

Suggested Citation

  • János Engländer, 2020. "A Generalization of the Submartingale Property: Maximal Inequality and Applications to Various Stochastic Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 506-521, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-019-00880-6
    DOI: 10.1007/s10959-019-00880-6
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    References listed on IDEAS

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    1. S. E. Graversen & G. Peškir, 1998. "Optimal Stopping and Maximal Inequalities for Linear Diffusions," Journal of Theoretical Probability, Springer, vol. 11(1), pages 259-277, January.
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