PROBABILISTIC APPROACH TO THE NEUMANN PROBLEM

(整期优先)网络出版时间:1990-02-12
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Inthispaper,weconsidertheNeumannboundaryvalueproblemofSchrodingeroperatorwithmeasurepotentia1μ.First,amartingaleformulationoftheNeumannproblemandananalyticcharacterizationofthemartingaleformulationaregiven.Then,byusingtheDirichletformsandStochasticanalysisweobtainanexplicitformulafortheuniqueweaksolotionofthisproblemintermsofreflectingBrownianmotionandit’sboundarylocaltime.