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Limit Distribution of the Banach Random Walk

Author

Listed:
  • Tadeusz Banek

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

  • Patrycja Jędrzejewska

    (The John Paul II Catholic University of Lublin)

  • August M. Zapała

    (The John Paul II Catholic University of Lublin)

Abstract

We consider various probability distributions $$\{G_n, n\ge 1\}$$ { G n , n ≥ 1 } concentrated on the interval $$[-1,1]\subset \mathbb {R}$$ [ - 1 , 1 ] ⊂ R and investigate basic properties of the limit distribution $$\Gamma $$ Γ of the Banach random walk in a Banach space $$\mathbb {B}$$ B generated by $$\{G_n , n\ge 1\}$$ { G n , n ≥ 1 } . In particular, we describe assumptions ensuring that the support of $$\Gamma $$ Γ is equal to the unit sphere in $$\mathbb {B}$$ B and, on the other hand, we find conditions under which every ball of radius smaller than 1 has a positive measure $$\Gamma $$ Γ .

Suggested Citation

  • Tadeusz Banek & Patrycja Jędrzejewska & August M. Zapała, 2019. "Limit Distribution of the Banach Random Walk," Journal of Theoretical Probability, Springer, vol. 32(1), pages 47-63, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-018-0858-5
    DOI: 10.1007/s10959-018-0858-5
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