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

Tadeusz Banek () and August M. Zapała ()
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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

Journal of Theoretical Probability, 2019, vol. 32, issue 2, 586-607

Abstract: 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\,

Keywords: Banach random walk; Martingale; Radon–Nikodym property; Quasi-orthogonal Schauder basis; Primary 60J15; 60B12; 60G42; Secondary 60G46 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-019-00890-4

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