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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Flows generated by stochastic differential equatio
 ns with reflection - Andrey Pilipenko (National Ac
 ademy of Sciences of Ukraine)
DTSTART;TZID=Europe/London:20240809T100000
DTEND;TZID=Europe/London:20240809T110000
UID:TALK215677AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/215677
DESCRIPTION:It is well known that SDE with smooth coefficients
  generates a flow of diffeomorphisms of Euclidean 
 space. Consider now a stochastic flow generated by
  SDE with reflection at the boundary of the domain
 . It appears that properties of reflective flows a
 re quite different from the properties of flows ge
 nerated by SDEs in the whole space. We will discus
 s the following distinctions that arise for any no
 n-trivial reflecting flow:\n&nbsp\;\n(a) reflectiv
 e flows are coalescing\;\n&nbsp\;\n(b) reflective 
 flows are not continuously differentiable\, but ha
 ve a Sobolev derivative\, which satisfies a non-st
 andard stochastic differential equation\;\n&nbsp\;
 \n(c) push-forward of an absolute continuous measu
 re under reflective flows contains non-trivial sin
 gular component.
LOCATION:External
CONTACT:
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