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A New Markov Selection Procedure for Degenerate Diffusions

Author

Listed:
  • V. S. Borkar

    (Tata Institute of Fundamental Research)

  • K. Suresh Kumar

    (Indian Institute of Technology Bombay)

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.

Suggested Citation

  • V. S. Borkar & K. Suresh Kumar, 2010. "A New Markov Selection Procedure for Degenerate Diffusions," Journal of Theoretical Probability, Springer, vol. 23(3), pages 729-747, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-009-0242-6
    DOI: 10.1007/s10959-009-0242-6
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