Banach Random Walk in the Unit Ball $$S\subset l^{2}$$ S ⊂ l 2 and Chaotic Decomposition of $$l^{2}\left( S,{{\mathbb {P}}}\right) $$ l 2 S, P

Tadeusz Banek ()
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Tadeusz Banek: Lublin University of Technology

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1728-1735

Abstract: Abstract A Banach random walk in the unit ball S in $$l^{2}$$ l 2 is defined, and we show that the integral introduced by Banach (Theory of the integral. Warszawa-Lwów, 1937) can be expressed as the expectation with respect to the measure $${{\mathbb {P}}}$$ P induced by this walk. A decomposition $$l^{2}\left( S,{{\mathbb {P}}}\right) =\bigoplus _{i=0}^{\infty } {{\mathfrak {B}}}_{i}$$ l 2 S , P = ⨁ i = 0 ∞ B i in terms of what we call Banach chaoses is given.

Keywords: Random walk; Orthogonal expansion; Legendre polynomials; 60K99; 60G50 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0620-1

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