Sufficient Conditions for a First Passage Time Process to be that of Brownian Motion
Keyword(s):
In this paper we assign a set of conditions to a strong Markov process and arrive at a differential equation analogous to the Kolmogorov equation. However, in this case the duration variable is the net distance travelled and the state variable is a time, a situation precisely opposite to that of Brownian motion. Solving this differential equation under certain boundary conditions produces the density function of the first passage times of Brownian motion with positive drift (see [1]), with the aid of which we define a new stochastic process.
2012 ◽
Vol 13
(01)
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pp. 1250014
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1952 ◽
Vol 211
(1106)
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pp. 431-443
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1989 ◽
Vol 3
(1)
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pp. 77-88
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2009 ◽
Vol 46
(1)
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pp. 181-198
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2005 ◽
Vol 38
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pp. 4097-4104
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2012 ◽
Vol 49
(02)
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pp. 549-565
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