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
Retrieve article from Numdam
XIV: 37, 332-342, LNM 784 (1980)
ROGERS, L.C.G.;
WILLIAMS, David
Time-substitution based on fluctuating additive functionals (Wiener-Hopf factorization for infinitesimal generators) (
Markov processes)
This is a first step towards the extension of
1436 to Markov processes with a general state space
Keywords: Wiener-Hopf factorizations,
Additive functionals,
Changes of timeNature: Original Retrieve article from Numdam
XV: 16, 227-250, LNM 850 (1981)
ROGERS, L.C.G.
Williams' characterization of the Brownian excursion law: proof and applications (
Brownian motion)
In the early eighties, Ito's rigorous approach to Lévy's ideas on excursions, aroused much enthusiasm, as people discovered it led to simple and conceptual proofs of most classical results on Brownian motion, and of many new ones. This paper contains the first published proof of the celebrated description of the Ito measure discovered by Williams (Williams
Diffusions, Markov Processes and Martingales, Wiley 1979, II.67), and it collects a number of applications, including the Azéma-Yor approach to Skorohod's imbedding theorem (
1306)
Keywords: Excursions,
Explicit laws,
Bessel processes,
Skorohod imbeddingNature: Original Retrieve article from Numdam
XVI: 04, 41-90, LNM 920 (1982)
LONDON, R.R.;
McKEAN, Henry P.;
ROGERS, L.C.G.;
WILLIAMS, David
A martingale approach to some Wiener-Hopf problems (two parts) Retrieve article from Numdam
XVIII: 03, 42-55, LNM 1059 (1984)
ROGERS, L.C.G.
Brownian local times and branching processes Retrieve article from Numdam
XXIII: 17, 186-197, LNM 1372 (1989)
ROGERS, L.C.G.
Multiple points of Markov processes in a complete metric space Retrieve article from Numdam
XLVII: 17, 321-338, LNM 2137 (2015)
DUEMBGEN, Moritz;
ROGERS, L. C. G.
The Joint Law of the Extrema, Final Value and Signature of a Stopped Random WalkNature: Original
