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Stochastic Integration Based on Simple, Symmetric Random Walks

Author

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  • Tamás Szabados

    (Budapest University of Technology and Economics)

  • Balázs Székely

    (Budapest University of Technology and Economics)

Abstract

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, the method gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not càdlàg in general.

Suggested Citation

  • Tamás Szabados & Balázs Székely, 2009. "Stochastic Integration Based on Simple, Symmetric Random Walks," Journal of Theoretical Probability, Springer, vol. 22(1), pages 203-219, March.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-007-0140-8
    DOI: 10.1007/s10959-007-0140-8
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    References listed on IDEAS

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    1. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
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    Cited by:

    1. Tamás Szabados, 2012. "Self-intersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1081-1118, December.

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