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Deviation inequalities for continuous martingales

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  • Khoshnevisan, Davar

Abstract

We consider a broad class of continuous martingales whose local modulus of continuity is in some sense deterministic. We show that such martingales have Gaussian probability tails, provided we appropriately normalize them by their quadratic variation. As other applications of our methods, we provide energy inequalities and prove a new sufficient condition for the joint continuity of continuous additive functionals of Brownian motion indexed by their Revuz measures.

Suggested Citation

  • Khoshnevisan, Davar, 1996. "Deviation inequalities for continuous martingales," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 17-30, December.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:17-30
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    1. Bass, Richard, 1984. "Joint continuity and representations of additive functionals of d-dimensional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 211-227, July.
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    Cited by:

    1. Naiqi Liu & Vladimir V. Ulyanov & Hanchao Wang, 2022. "On De la Peña Type Inequalities for Point Processes," Mathematics, MDPI, vol. 10(12), pages 1-13, June.

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