2 results
On level crossings for a general class of piecewise-deterministic Markov processes
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- Journal:
- Advances in Applied Probability / Volume 40 / Issue 3 / September 2008
- Published online by Cambridge University Press:
- 01 July 2016, pp. 815-834
- Print publication:
- September 2008
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We consider a piecewise-deterministic Markov process (Xt) governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. The paper deals with the point process
of upcrossings of some level b by (Xt). We prove a version of Rice's formula relating the stationary density of (Xt) to level crossing intensities and show that, for a wide class of processes (Xt), as b → ∞, the scaled point process 
where ν+(b) denotes the intensity of upcrossings of b, converges weakly to a geometrically compound Poisson process.
of upcrossings of some level 
where νCompound Poisson limit theorems for Markov chains
- Part of
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- Journal:
- Journal of Applied Probability / Volume 34 / Issue 1 / March 1997
- Published online by Cambridge University Press:
- 14 July 2016, pp. 24-34
- Print publication:
- March 1997
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