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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.
|Translated title of the contribution||Excursions of diffusion processes and continued fractions|
|Pages (from-to)||850 - 874|
|Number of pages||25|
|Journal||Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques|
|Volume||47, number 3|
|Publication status||Published - Aug 2011|