Probabilistic Solution of the General Robin Boundary Value Problem on Arbitrary Domains
2012 ◽
Vol 2012
◽
pp. 1-17
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Keyword(s):
Using a capacity approach and the theory of the measure’s perturbation of the Dirichlet forms, we give the probabilistic representation of the general Robin boundary value problems on an arbitrary domain Ω, involving smooth measures, which give rise to a new process obtained by killing the general reflecting Brownian motion at a random time. We obtain some properties of the semigroup directly from its probabilistic representation, some convergence theorems, and also a probabilistic interpretation of the phenomena occurring on the boundary.
2020 ◽
Vol 35
(4)
◽
pp. 410-416
2004 ◽
Vol 207
(2)
◽
pp. 303-359
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2015 ◽
Vol 2015
◽
pp. 1-15
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2020 ◽
Vol 79
(10)
◽
pp. 2805-2818
1998 ◽
Vol 56
(2)
◽
pp. 245-257
◽
2015 ◽