On the Last Zero of a Wiener Process

K. Grill
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K. Grill: Technical University

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 99-104 from Springer

Abstract: Abstract Let (W(t), t ≥ 0) be a standard Wiener process; denote by M(t) the maximum of its modulus before t and by Z(t) the last root of W(.) before t. The lower limiting behaviour of these quantities has been studied by various authors, theorems by Chung (1948, the so-called “second law of the iterated logarithm”) and Chung-Erdõs (1952) give integral characterizations for the lower limiting classes. In the present paper we study how small these quantities can simultaneously get, or, in other words, how small one can get if the other is known to be small.

Keywords: Independent Random Variable; Wiener Process; Iterate Logarithm; Standard Wiener Process; Monotonicity Assumption (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_9

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DOI: 10.1007/978-94-009-3963-9_9

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