Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part

Authors:	Email author" target="_blank">Gerald?Trutnau Email author

Institution:	(1) Université Paris 13, Département de Mathématiques, Institut Galilée, 99, av. Jean-Baptiste Clément, 93430 Villetaneuse, France

Abstract:	Let ${{\overline{{G}}\subset {{\mathbb R}}^d}}$ be a compact set with interior G. Let L ¹(G,dx), >0 dx-a.e. on G, and m:=dx. Let A=(a _ij) be symmetric, and globally uniformly strictly elliptic on G. Let be such that ${{{{{{\mathcal E}}}}^r(f,g)=\frac{{1}}{{2}}\sum_{{i,j=1}}^{{d}}\int_G a_{{ij}}\partial_i f \partial_j g\,dm}}$ ; f, ${{g\in C^{{\infty}}(\overline{{G}})}}$ , is closable in L ²(G,m) with closure (^r,D(^r)). The latter is fulfilled if satisfies the Hamza type condition, or _iL ¹ _loc(G,dx), 1id. Conservative, non-symmetric diffusion processes X _t related to the extension of a generalized Dirichlet form ${{ {{{{\mathcal E}}}}^r(f,g) -\sum_{{i=1}}^{{d}}\int_G \rho^{{-1}}\overline{{B}}_i\partial_i f\, g\, dm; f,g\in D({{{{\mathcal E}}}}^r)_b }}$ where ${{\rho^{{-1}}(\overline{{B}}_1,...,\overline{{B}}_d)\in L^2(G;{{\mathbb R}}^d,m)}}$ satisfies ${{ \sum_{{i=1}}^{{d}}\int_G \overline{{B}}_i \partial_i f\,dx =0\quad {{\rm{ for all}}} f\in C^{{\infty}}(\overline{{G}}), }}$ are constructed and analyzed. If G is a bounded Lipschitz domain, H ^1,1(G), and a _ijD(^r), a Skorokhod decomposition for X _t is given. This happens through a local time that is uniquely associated to the smooth measure 1_{ _Tr _()>0} d, where Tr denotes the trace and the surface measure on G.This research has been financially supported by TMR grant HPMF-CT-2000-00942 of the European Union. Mathematics Subject Classification (2000): 60J60, 60J55, 31C15, 31C25, 35J25

Keywords:	Diffusion processes Local time and additive functionals Potential and capacities Dirichlet spaces Boundary value problems for second order elliptic operators
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