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First Passage Time Distribution of a Two-Dimensional Wiener Process with Drift

Published online by Cambridge University Press:  27 July 2009

Marco Dominé  and
Volkmar Pieper
Marco Dominé
Affiliation:
Department of Mathematical Stochastics, Technical University of Magdeburg, PSF 4120, 39076 Magdeburg, Germany
Volkmar Pieper
Affiliation:
Department of Mathematical Stochastics, Technical University of Magdeburg, PSF 4120, 39076 Magdeburg, Germany
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Abstract

The two-dimensional correlated Wiener process (or Brownian motion) with drift is considered. The Fokker-Planck (or Kolmogorov forward) equation for the Wiener process (X1(t), X2(t)) is solved under absorbing boundary conditions on the lines x1= h1 and x2 = h2 and a fixed starting point (x0,1, x0,2). The first passage (or first exit) time when the process leaves the domain G = ( −∞, h1) × ( −∞, h2) is derived.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 4 , October 1993 , pp. 545 - 555
Copyright
Copyright © Cambridge University Press 1993

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