A New Markov Selection Procedure for Degenerate Diffusions

V. S. Borkar () and K. Suresh Kumar ()
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V. S. Borkar: Tata Institute of Fundamental Research
K. Suresh Kumar: Indian Institute of Technology Bombay

Journal of Theoretical Probability, 2010, vol. 23, issue 3, 729-747

Abstract: Abstract A new selection principle is proposed for construction of a Feller solution to an ill-posed degenerate diffusion process. This is based on constructing the Feller transition kernel from the unique (under suitable conditions) continuous viscosity solutions to the backward Kolmogorov equation associated with the diffusion. The connection of this Feller process with the small-noise limits of the nondegenerate perturbations of the diffusion and several other related phenomena are also discussed.

Keywords: Degenerate diffusions; Markov selection; Feller process; Small noise limit; Backward Kolmogorov equation; Viscosity solutions; 60H10; 60J25; 34F05; 35K65 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0242-6

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