Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection
Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods, regularity for solutions of elliptic boundary value problems, construction of elliptic diffusions with singular drift and reflection, Skorokhod decomposition and applications to Mathematical Physics like finite particle systems with singular interaction. Emphasize is placed on the handling of singular drift coefficients, as well as on the discussion of point wise and path wise properties of the constructed processes rather than just the quasi-everywhere properties commonly known from the general Dirichlet form theory.
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Elliptic Boundary Value Problems and Construction of LP-Strong Feller ...
No preview available - 2014
a e E1 absolutely continuous additive functionals additivity set apply Assume assumptions Borel measure bounded variation Brownian motion C*-smooth cape Choose coefficients compact separable metric compact set Condition continuous version convergence Corollary CP(E Define Definition denote density diffusion DNeu fulfills Furthermore gradient Dirichlet form hence Hölder continuous holds implies integral kernels Lebesgue measure Lemma Let u e linear operator Lipschitz smooth locally compact locally of bounded LP-resolvent Lp-Strong Feller Processes LP(E LP(Q mapping Markov property martingale problem matrix metric space norm Note open sets paths point separating pointwise probability measure Proof prove Q C R Revuz correspondence right-continuous Section segment property semigroup semimartingale singular drift Sobolev space solves the martingale stochastic strict finite PCAF strong Feller subset symmetric Theo Theorem u e D(Lp weak derivatives weak solutions