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Transportation inequalities for stochastic differential equations with jumps

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  • Ma, Yutao

Abstract

For stochastic differential equations with jumps, we prove that W1H transportation inequalities hold for their invariant probability measures and for their process-level laws on the right-continuous path space w.r.t. the L1-metric and uniform metric, under dissipative conditions, via Malliavin calculus. Several applications to concentration inequalities are given.

Suggested Citation

  • Ma, Yutao, 2010. "Transportation inequalities for stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 2-21, January.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:1:p:2-21
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    Cited by:

    1. Torrisi, Giovanni Luca, 2020. "Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6445-6479.
    2. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Dejun Luo, 2015. "Quasi-invariance of the Stochastic Flow Associated to Itô’s SDE with Singular Time-Dependent Drift," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1743-1762, December.
    4. Suo, Yongqiang & Yuan, Chenggui & Zhang, Shao-Qin, 2022. "Transportation cost inequalities for SDEs with irregular drifts," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 288-311.

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