Characterizing Gaussian Flows Arising from Itô’s Stochastic Differential Equations

Bhar, Suprio

doi:10.1007/s11118-016-9578-6

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2019

2023

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Cited by 2 publications

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“…However, the multiplication operators that intervene in the definition of L * and A * create significant difficulties in proving these inequalities because of their non self adjointness in these spaces. Uniqueness for the Gaussian case can however be handled by special methods (see [1]). For some background on the 'Monotonicity inequality' we refer to [2,6,7,15,19,22].…”

Section: Introductionmentioning

confidence: 99%

Solutions of SPDE’s Associated with a Stochastic Flow

2019

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We consider the following stochastic partial differential equation, Potential Anal. 28 (2008), no. 2, 139-162]. We show that the strong solutions constructed there are 'locally of compact support'. Using this notion,we define the mild solutions of the above equation and show the equivalence between strong and mild solutions in the multi Hilbertian space S ′ . We show uniqueness of solutions in the case when ψ is smooth via the 'monotonicity inequality' for (L * , A * ), which is a known criterion for uniqueness. R d ψ(x)δ X(t,x) dx.

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Section: Introductionmentioning

confidence: 99%