A note on a.s. finiteness of perpetual integral functionals of diffusions

2005/11/14 by Paavo Salminen, Marc Yor, Salminen, Paavo +1 · 1 citation
Computer Science · Mathematics · #60J60 #60J65 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #advanced mathematical theories

paper · doi:10.48550/arxiv.math/0511336

openalex publication_date 2005/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, with the help of the boundary classification of diffusions, we derive a criterion of the convergence of perpetual integral functionals of transient real-valued diffusions. In the particular case of transient Bessel processes, we note that this criterion agrees with the one obtained via Jeulin's convergence lemma.

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