XIV: 36, 324-331, LNM 784 (1980)
BARLOW, Martin T.;
ROGERS, L.C.G.;
WILLIAMS, David
Wiener-Hopf factorization for matrices (
Markov processes)
Let $(X_t)$ be a continuous-time Markov chain with a finite state space $E$, and a transition semigroup $\exp(tQ)$. Consider the fluctuating additive functional $\phi_t=\int_0^t v(X_s)\,ds$ ($v$ is a function on $E$ which may assume negative values) and the corresponding change of time $\tau_t= \inf\{s:\phi_s>t\}$. The problem is to find the joint distribution of $\tau_t$ and $X(\tau_t)$. This is solved using martingale methods, and implies a purely algebraic result on the structure of the Q-matrix
Comment: A mistake is pointed out by the authors at the end of the paper, and is corrected in
1437Keywords: Wiener-Hopf factorizations,
Additive functionals,
Changes of time,
Markov chainsNature: Original
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