Phase transition for absorbed Brownian motion with drift

Journal of Statistical Physics

Volumn 86, Issue 1-2, 1997, Pages 213-231

  Ferrari, P A ^a   Martinez, S ^b   San Martin J ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b DEPARTAMENTO DE FÍSICA   (Chile)

Author keywords

Absorbed brownian motion; Conditioned brownian motion with drift; Quasistationary distributions

Indexed keywords

EID: 0030676804     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02180205     Document Type: Article

References (10)

1. J. A. Cavender, Quasi-stationary distributions of birth and death processes, Adv. Appl. Prob. 10:570-586 (1978).
2. R. T. Durrett, D. L. Iglehart, and D. R. Miller, Weak convergence to Brownian meander and Brownian excursion, Ann. Prob. 5(1):117-229 (1977).
3. P. A. Ferrari, H. Kesten, S. Martínez, and P. Picco, Existence of quasi stationary distribu√ tions. A renewal dynamical approach, Ann. Prob. 23(2):501-521 (1995).
4. P. A. Ferrari, H. Kesten, and S. Martínez, R-Positivity, quasi stationary and ratio limit theorem for a class of probabilistic automata, Ann. Appl. Prob., to appear (1996).
5. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus (Springer-Verlag, Berlin, 1988).
6. S. Martínez and J. San Martín, Quasi-stationary distributions for a Brownian motion with drift and associated limit laws, J. Appl. Prob. 31(4):911-920 (1994).
7. H. Scheffé, A useful convergence theorem for probability distributions, Ann. Math. Stat. XVIII(3):434-438 (1947).
8. E. Seneta, Quasi-stationary behaviour in the random walk with continuous time, Austral. J. Statist. 8:92-98 (1966).
9. D. Vere-Jones, Geometric ergodicity in denumerable Markov chains, Q. J. Math. Oxford 2 13:7-28 (1962).
10. A. M. Yaglom, Certain limit theorems of the theory of branching stochastic processes, Dokl. Akad. Nauk SSSR (N.S.) 56:795-798 (1947).