How the sojourn time distributions of Brownian motion are affected by different forms of conditioning

L. Beghin, Yakov Nikitin and E. Orsingher

Statistics & Probability Letters, 2003, vol. 65, issue 4, 291-302

Abstract: In this paper we study the distribution of the sojourn time [Gamma]t=meas{s 0}, where B(t), t>0 is a Brownian motion (with or without drift), under different conditions at an intermediate time u[less-than-or-equals, slant]t (and possibly with an additional condition at time t). We obtain different forms of the arc-sine law, which display a "bell-shaped" structure (instead of the usual "U-shaped" classical density) when (B(u)=0) is assumed. When the conditions (B(u)=0,B(t)[greater, less]0) are taken into account, an asymmetrical bell-shaped density is obtained.

Keywords: Brownian; motion; Sojourn; time; Arc-sine; law; Feynman-Kac; functional (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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