Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations

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• 作者：Suprio Bhar
• 关键词：Gaussian flows ; Stochastic flows ; Diffusion processes ; Stochastic differential equations ; Forward equations ; Monotonicity inequality
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：46
• 期：2
• 页码：261-277
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

In order to identify which of the strong solutions of Itô’s stochastic differential equations (SDEs) are Gaussian, we introduce a class of diffusions which ‘depend deterministically on the initial condition’ and then characterize the class. This characterization allows us to show, using the Monotonicity inequality, that the transpose of the flows generated by the SDEs, for an extended class of initial conditions, are the unique solutions of the class of stochastic partial differential equations introduced in Rajeev and Thangavelu (Potential Anal. 28(2), 139–162 2008), ‘Probabilistic Representations of Solutions of the Forward Equations’.