An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control

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An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control

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作者：H. Abels ; M. Kassmann
关键词：Bellman equation ; Fully nonlinear equation ; Integro-differential operator ; Markov jump process ; Stochastic control
刊名：Journal of Differential Equations
出版年：2007
出版时间：1 May 2007
年：2007
卷：236
期：1
页码：29-56
全文大小：275 K

文摘

Given a bounded domain and two integro-differential operators J2-4MSPV7R-5&_mathId=mml2&_user=10&_cdi=6866&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=bc0f36eb6c5a19c73bef7573f5149302"" title=""Click to view the MathML source"">Lp>1p>, Lp>2p> of the form l4""> we study the fully nonlinear Bellman equation

with Dirichlet boundary conditions. Here, are non-negative functions. We prove the existence of a non-negative function which satisfies (0.1) almost everywhere. The main difficulty arises through the nonlocality of Lp>jp> and the absence of regularity near the boundary.

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