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Some remarks on local time-space calculus

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  • Yang, Xiangfeng
  • Yan, Litan

Abstract

Let X be a reversible semi-martingale satisfying certain conditions and let be a locally bounded measurable function such that it admits locally bounded Radon-Nikodym derivatives [not partial differential]F/[not partial differential]t and [not partial differential]F/[not partial differential]x, then the following change-of-variable formula is valid: where is the local time of X at x, and denotes the stochastic area integral with respect to defined by Eisenbaum [2006. Local time-space stochastic calculus for Lévy processes. Stochastic process and Appl. 116, 757-778]. Furthermore, some results are extended from deterministic integrated functions to random functions. We establish the conditions for the existence of such stochastic area integration and give some representations of this integral.

Suggested Citation

  • Yang, Xiangfeng & Yan, Litan, 2007. "Some remarks on local time-space calculus," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1600-1607, October.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:16:p:1600-1607
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    References listed on IDEAS

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    1. Eisenbaum, Nathalie, 2006. "Local time-space stochastic calculus for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 757-778, May.
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