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Random Walk in Balls and an Extension of the Banach Integral in Abstract Spaces

Author

Listed:
  • Tadeusz Banek

    (Pope John Paul II State School of Higher Education in Biała Podlaska)

  • August M. Zapała

    (The John Paul II Catholic University of Lublin)

Abstract

We describe the construction of a random walk in a Banach space $$\mathbb {B}$$ B with a quasi-orthogonal Schauder basis and show that it is a martingale. Next we prove that under certain additional assumptions the described random walk converges a.s. and in $$L^{p}\left( \mathbb {B}\right) ,\,1\le p\,

Suggested Citation

  • Tadeusz Banek & August M. Zapała, 2019. "Random Walk in Balls and an Extension of the Banach Integral in Abstract Spaces," Journal of Theoretical Probability, Springer, vol. 32(2), pages 586-607, June.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-019-00890-4
    DOI: 10.1007/s10959-019-00890-4
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