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Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type

Author

Listed:
  • Yuichi Shiozawa

    (Osaka University)

  • Jian Wang

    (Fujian Normal University)

Abstract

We present sufficient conditions, in terms of the jumping kernels, for two large classes of conservative Markov processes of pure-jump type to be purely discontinuous martingales with finite second moment. As an application, we establish the law of the iterated logarithm for sample paths of the associated processes.

Suggested Citation

  • Yuichi Shiozawa & Jian Wang, 2021. "Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2005-2032, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01035-8
    DOI: 10.1007/s10959-020-01035-8
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    References listed on IDEAS

    as
    1. Kim, Panki & Lee, Jaehun, 2019. "Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2130-2173.
    2. Wang, Jia-gang, 1993. "A law of the iterated logarithm for stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 215-228, September.
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