Moment Generating Functions for Local Times of Symmetric Markov Processes and Random Walks

  • Michael B. Marcus
  • Jay Rosen
Chapter
Part of the Progress in Probability book series (PRPR, volume 30)

Abstract

We obtain moment generating functions for the local times of strongly symmetric Markov processes and symmetric random walks via the Dynkin Isomorphism Theorem. This allows us to reduce complex computations involving Markov processes to elementary manipulations of Gaussian random variables.

Keywords

Covariance Rosen 

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References

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    Dynkin, E.B. (1983) Local times and quantum fields, In: Seminar on stochastic processes (E. Çinlar, K.L. Chung, R.K. Getoor, Eds), Birkhäuser, Boston.Google Scholar
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    Dynkin, E.B. (1984) Gaussian and non-Gaussian random fields associated with Markov processes, J. Funct. Anal. 55, 344–376.MathSciNetMATHCrossRefGoogle Scholar
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    Fitzsimmons, P. and Getoor, R. (1991) On the distribution of the Hilbert transform of the local time of a symmetric Lévy process, preprint.Google Scholar
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    Marcus, M. and Rosen, J. (1990) Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes, preprint.Google Scholar
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    Marcus, M. and Rosen, J. (1991) Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks, preprint.Google Scholar
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    Rosen, J. (1990) Second order limit laws for the local times of stable processes, preprintGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Michael B. Marcus
    • 1
  • Jay Rosen
    • 2
  1. 1.Department of MathematicsThe City College of CUNYNew YorkUSA
  2. 2.Department of MathematicsCollege of Staten Island, CUNYStaten IslandUSA

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