Limit Distribution of the Banach Random Walk

Tadeusz Banek (), Patrycja Jędrzejewska () and August M. Zapała ()
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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

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 47-63

Abstract: 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 .

Keywords: Banach random walk; Limit distribution; Support of the measure; Quasi-orthogonal Schauder basis; 60J15; 60B12; 60G42; 60G46 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0858-5

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