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Detailed probabilistic analysis of the integrated three-valued telegraph signal
- Part of
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- Journal:
- Journal of Applied Probability / Volume 34 / Issue 3 / September 1997
- Published online by Cambridge University Press:
- 14 July 2016, pp. 671-684
- Print publication:
- September 1997
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- Article
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In this paper the integrated three-valued telegraph process
is examined. In particular, the third-order equations governing the distributions 
, (where N(t) denotes the number of changes of the telegraph process up to time t) are derived and recurrence relationships for them are obtained by solving suitable initial-value problems. These recurrence formulas are related to the Fourier transform of the conditional distributions and are used to obtain explicit results for small values of k. The conditional mean values 
(where V(0) denotes the initial velocity of motions) are obtained and discussed.
is examined. In particular, the third-order equations governing the distributions 
, (where 
(where 