An Arc-Sine Law for Last Hitting Points in the Two-Parameter Wiener Space

Jeong-Gyoo Kim
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Jeong-Gyoo Kim: School of Games, Hongik University, Sejong 30016, Korea

Mathematics, 2019, vol. 7, issue 11, 1-11

Abstract: We develop the two-parameter version of an arc-sine law for a last hitting time. The existing arc-sine laws are about a stochastic process X t with one parameter t . If there is another varying key factor of an event described by a process, then we need to consider another parameter besides t . That is, we need a system of random variables with two parameters, say X s , t , which is far more complex than one-parameter processes. In this paper we challenge to develop such an idea, and provide the two-parameter version of an arc-sine law for a last hitting time. An arc-sine law for a two-parameter process is hardly found in literature. We use the properties of the two-parameter Wiener process for our development. Our result shows that the probability of last hitting points in the two-parameter Wiener space turns out to be arcsine-distributed. One can use our results to predict an event happened in a system of random variables with two parameters, which is not available among existing arc-sine laws for one parameter processes.

Keywords: arc-sine law; last hitting points; two-parameter Wiener space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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