Excursions of diffusion processes and continued fractions

A Comtet; YJM Tourigny

doi:10.1214/10-AIHP390

Excursions of diffusion processes and continued fractions

A Comtet, YJM Tourigny

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

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.

Translated title of the contribution	Excursions of diffusion processes and continued fractions
Original language	English
Pages (from-to)	850 - 874
Number of pages	25
Journal	Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume	47, number 3
DOIs	https://doi.org/10.1214/10-AIHP390
Publication status	Published - Aug 2011

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SERIES SUMMATION AND RANDOM CONTINUED FRACTIONS
Tourigny, Y. J. M. (Principal Investigator)
1/08/04 → 1/01/08
Project: Research

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title = "Excursions of diffusion processes and continued fractions",

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 = "A Comtet and YJM Tourigny",

year = "2011",

month = aug,

doi = "10.1214/10-AIHP390",

language = "English",

volume = "47, number 3",

pages = "850 -- 874",

journal = "Annales de l'Institut Henri Poincar{\'e} (B) Probabilit{\'e}s et Statistiques",

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TY - JOUR

T1 - Excursions of diffusion processes and continued fractions

AU - Comtet, A

AU - Tourigny, YJM

PY - 2011/8

Y1 - 2011/8

N2 - 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.

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.

U2 - 10.1214/10-AIHP390

DO - 10.1214/10-AIHP390

M3 - Article (Academic Journal)

VL - 47, number 3

SP - 850

EP - 874

JO - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

ER -

Excursions of diffusion processes and continued fractions

Abstract

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SERIES SUMMATION AND RANDOM CONTINUED FRACTIONS

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