Solutions of SPDE’s Associated with a Stochastic Flow View Full Text


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Article Info

DATE

2019-02-02

AUTHORS

Suprio Bhar, Rajeev Bhaskaran, Barun Sarkar

ABSTRACT

We consider the following stochastic partial differential equation, dYt=L∗Ytdt+A∗Yt⋅dBtY0=ψ,associated with a stochastic flow {X(t,x)}, for t ≥ 0, x∈ℝd, as in Rajeev and Thangavelu (Potential Anal. 28(2), 139–162, 2008). 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. More... »

PAGES

1-19

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11118-019-09764-0

DOI

http://dx.doi.org/10.1007/s11118-019-09764-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111893472


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