Electronic Journal of Probability

Harnack inequalities for stochastic (functional) differential equations with non-Lipschitzian coefficients

Jinghai Shao, Feng-Yu Wang, and Chenggui Yuan

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By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two results on existence and uniqueness of solutions on an open domain are presented.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 100, 18 pp.

Accepted: 23 November 2012
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60J60: Diffusion processes [See also 58J65] 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]

Harnack inequality log-Harnack inequality stochastic (functional) differential equation existence and uniqueness

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Shao, Jinghai; Wang, Feng-Yu; Yuan, Chenggui. Harnack inequalities for stochastic (functional) differential equations with non-Lipschitzian coefficients. Electron. J. Probab. 17 (2012), paper no. 100, 18 pp. doi:10.1214/EJP.v17-2140. https://projecteuclid.org/euclid.ejp/1465062422

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