Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations
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’.
Bhar, Suprio, "Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations" (2017). Journal Articles. 2709.