Excursions of diffusion processes and continued fractions

Alain Comtet; Yves Tourigny

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 850-874
  • ISSN: 0246-0203

Abstract

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It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.

How to cite

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Comtet, Alain, and Tourigny, Yves. "Excursions of diffusion processes and continued fractions." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 850-874. <http://eudml.org/doc/242204>.

@article{Comtet2011,
abstract = {It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.},
author = {Comtet, Alain, Tourigny, Yves},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {diffusion processes; continued fraction; Riccati equation; excursions; Stieltjes transform},
language = {eng},
number = {3},
pages = {850-874},
publisher = {Gauthier-Villars},
title = {Excursions of diffusion processes and continued fractions},
url = {http://eudml.org/doc/242204},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Comtet, Alain
AU - Tourigny, Yves
TI - Excursions of diffusion processes and continued fractions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 850
EP - 874
AB - It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.
LA - eng
KW - diffusion processes; continued fraction; Riccati equation; excursions; Stieltjes transform
UR - http://eudml.org/doc/242204
ER -

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