期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 130, 期 10, 页码 6226-6245出版社
ELSEVIER
DOI: 10.1016/j.spa.2020.05.008
关键词
Stochastic partial differential equations; Fundamental solution; Parametrix method; Kolmogorov equation
资金
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)
We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in Holder classes and estimates from above and below of the fundamental solution. This result is applied to SPDEs by means of the Ito-Wentzell formula, through a random change of variables which transforms the SPDE into a PDE with random coefficients. (C) 2020 Elsevier B.V.All rights reserved.
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