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Harnack inequality for mean-field stochastic differential equations

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  • Zong, Gaofeng
  • Chen, Zengjing

Abstract

Buckdahn et al. (2009b) introduced a mean-field stochastic differential equation to study the backward stochastic differential equation. The objective of the present paper is to deepen the investigation of such mean-field stochastic differential equations by studying them in a Brownian motion framework. By constructing a coupling, log-Harnack inequality and Harnack inequality with dimension-free are established for such mean-field stochastic differential equations.

Suggested Citation

  • Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:5:p:1424-1432
    DOI: 10.1016/j.spl.2013.01.035
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    References listed on IDEAS

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    1. Wang, Feng-Yu & Yuan, Chenggui, 2011. "Harnack inequalities for functional SDEs with multiplicative noise and applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2692-2710, November.
    2. Li, Zhi & Luo, Jiaowan, 2012. "Mean-field reflected backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1961-1968.
    3. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    4. Arnaudon, Marc & Thalmaier, Anton & Wang, Feng-Yu, 2009. "Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3653-3670, October.
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