A Liouville theorem for Lévy generators
Copyright policy )A Liouville theorem for Lévy generators
AbstractUnder mild assumptions, we establish a Liouville theorem for the “Laplace” equation $$Au=0$$ A u = 0 associated with the infinitesimal generator A of a Lévy process: If u is a weak solution to $$Au=0$$ A u = 0 which is at most of (suitable) polynomial growth, then u is a polynomial. As a by-product, we obtain new regularity estimates for semigroups associated with Lévy processes.
- TU Dresden Germany
- TU Dresden Germany
- TU Dresden Germany
Lévy process, Probability (math.PR), Transition functions, generators and resolvents, Processes with independent increments; Lévy processes, Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs, pseudo-differential operator, Harmonic, subharmonic, superharmonic functions on other spaces, Integro-partial differential equations, 60G51, 35B53, 31C05, 35R09, 60J35, Mathematics - Analysis of PDEs, FOS: Mathematics, Liouville theorem, Mathematics - Probability, Analysis of PDEs (math.AP)
Lévy process, Probability (math.PR), Transition functions, generators and resolvents, Processes with independent increments; Lévy processes, Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs, pseudo-differential operator, Harmonic, subharmonic, superharmonic functions on other spaces, Integro-partial differential equations, 60G51, 35B53, 31C05, 35R09, 60J35, Mathematics - Analysis of PDEs, FOS: Mathematics, Liouville theorem, Mathematics - Probability, Analysis of PDEs (math.AP)
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