Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part
Let be a compact set with interior G. Let ρ∈L1(G,dx), ρ>0 dx-a.e. on G, and m:=ρdx. Let A=(aij) be symmetric, and globally uniformly strictly elliptic on G. Let ρ be such that ; f, , is closable in L2(G,m) with closure (ℰr,D(ℰr)). The latter is fulfilled if ρ satisfies the Hamza type condition, o...
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Published in | Probability theory and related fields Vol. 127; no. 4; pp. 455 - 495 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer
01.12.2003
Berlin Springer Nature B.V New York, NY |
Subjects | |
Online Access | Get full text |
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Summary: | Let be a compact set with interior G. Let ρ∈L1(G,dx), ρ>0 dx-a.e. on G, and m:=ρdx. Let A=(aij) be symmetric, and globally uniformly strictly elliptic on G. Let ρ be such that ; f, , is closable in L2(G,m) with closure (ℰr,D(ℰr)). The latter is fulfilled if ρ satisfies the Hamza type condition, or ∂iρ∈L1loc(G,dx), 1≤i≤d. Conservative, non-symmetric diffusion processes Xt related to the extension of a generalized Dirichlet form where satisfies are constructed and analyzed. If G is a bounded Lipschitz domain, ρ∈H1,1(G), and aij∈D(ℰr), a Skorokhod decomposition for Xt is given. This happens through a local time that is uniquely associated to the smooth measure 1{Tr(ρ)>0}dΣ, where Tr denotes the trace and Σ the surface measure on ∂G. |
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ISSN: | 0178-8051 1432-2064 |
DOI: | 10.1007/s00440-003-0296-9 |