Open Access
May, 1985 Excursion Laws of Markov Processes in Classical Duality
H. Kaspi
Ann. Probab. 13(2): 492-518 (May, 1985). DOI: 10.1214/aop/1176993005


We study excursion laws of two Markov processes $X, \hat{X}$ in duality, out of closed, homogeneous optional sets $M, \hat{M}$ generated by a pair of dual terminal times $R$ and $\hat{R}$. The duality assumptions enable one to compute the laws of $(R, X_R)$ using the pair of exit systems of the two processes. With this, one is able to compute the conditional laws of the excursions, given the boundary process. It turns out that these depend only on the values of the boundary process at the beginning and end of the excursions. We obtain for all $x, y(x \neq y)$ the laws $p^{x,y}$ of the excursions conditioned to start at $x$ and end at $y$. Under these laws, the excursion process is a homogeneous Markov process. It's transition laws are computed. We use the results above to treat excursions that straddle perfect terminal times.


Download Citation

H. Kaspi. "Excursion Laws of Markov Processes in Classical Duality." Ann. Probab. 13 (2) 492 - 518, May, 1985.


Published: May, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0566.60075
MathSciNet: MR781419
Digital Object Identifier: 10.1214/aop/1176993005

Primary: 60J60
Secondary: 60J45

Keywords: excursion laws , exit systems , Markov processes in duality

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • May, 1985
Back to Top