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Random Walks Associated with Non-Divergence Form Elliptic Equations

Author

Listed:
  • Joseph G. Conlon

    (University of Michigan)

  • Renming Song

    (University of Illinois)

Abstract

This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d≥2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d−1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d−1 dimensional manifolds which are C 1, α , and also d−1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.

Suggested Citation

  • Joseph G. Conlon & Renming Song, 2000. "Random Walks Associated with Non-Divergence Form Elliptic Equations," Journal of Theoretical Probability, Springer, vol. 13(2), pages 427-489, April.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:2:d:10.1023_a:1007893424255
    DOI: 10.1023/A:1007893424255
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    References listed on IDEAS

    as
    1. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    2. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
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