First Passage Time Distribution of a Two-Dimensional Wiener Process with Drift
- 1 January 1993
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 7 (4) , 545-555
- https://doi.org/10.1017/s0269964800003120
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 linesx1=h1andx2=h2and a fixed starting point (x0,1,x0,2). The first passage (or first exit) time when the process leaves the domainG= ( −∞,h1) × ( −∞,h2) is derived.Keywords
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