Integrability conditions for SDEs and semilinear SPDEs

• Feng-Yu Wang ^[1]
  1. [1] Tianjin University

     Tianjin University

     China

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 5, 2017, págs. 3223-3265
• Idioma: inglés
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• Resumen

  • By using the local dimension-free Harnack inequality established on incomplete Riemannian manifolds, integrability conditions on the coefficients are presented for SDEs to imply the nonexplosion of solutions as well as the existence, uniqueness and regularity estimates of invariant probability measures. These conditions include a class of drifts unbounded on compact domains such that the usual Lyapunov conditions cannot be verified. The main results are extended to second-order differential operators on Hilbert spaces and semilinear SPDEs.