Quasi-stationary distributions for a Brownian motion with drift and associated limit laws
Authors:
- Servet MartinezSMServet Martinez
- Jaime San MartinJMJaime San Martin
- 1 December 1994
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 31 (4) , 911-920
Abstract
We prove that the quasi-invariant measures associated to a Brownian motion with negative drift X form a one-parameter family. The minimal one is a probability measure inducing the transition density of a three-dimensional Bessel process, and it is shown that it is the density of the limit distribution limt→∞Px(X A | τ > t). It is also shown that the minimal quasi-invariant measure of infinite mass induces the density of the limit distribution ) which is the law of a Bessel process with drift.Keywords
This publication has 9 references indexed in Scilit:
- Existence of non-trivial quasi-stationary distributions in the birth-death chainAdvances in Applied Probability, 1992
- Limit Theorems for Random Walks Conditioned to Stay PositiveThe Annals of Probability, 1992
- Brownian Motion and Stochastic Calculus1988
- Markov FunctionsThe Annals of Probability, 1981
- Quasi-stationary distributions of birth-and-death processesAdvances in Applied Probability, 1978
- Decomposing the Brownian pathBulletin of the American Mathematical Society, 1970
- Brownian local times and taboo processesTransactions of the American Mathematical Society, 1969
- On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of statesJournal of Applied Probability, 1966
- GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINSThe Quarterly Journal of Mathematics, 1962