Khoshnevisan, Davar; Salminen, Paavo; Yor, Marc A note on a.s. finiteness of perpetual integral functionals of diffusions. (English) Zbl 1111.60061 Electron. Commun. Probab. 11, 108-117 (2006). Summary: We use the boundary classification of diffusions in order to derive a criterion for the convergence of perpetual integral functionals of transient real-valued diffusions. We present a second approach, based on R. Khas’minskij’s lemma [Theor. Probab. Appl. 4, 309–318 (1960); translation from Teor. Veroyatn. Primen. 4, 332–341 (1959; Zbl 0089.34501)], which is applicable also to spectrally negative Lévy processes. In the particular case of transient Bessel processes, our criterion agrees with the one obtained via T. Jeulin’s convergence lemma [in: Séminaire de probabilités XVI. Lect. Notes Math. 920, 248–256 (1982; Zbl 0483.60020)]. Cited in 15 Documents MSC: 60J60 Diffusion processes 60J65 Brownian motion Citations:Zbl 0483.60020; Zbl 0089.34501 × Cite Format Result Cite Review PDF Full Text: DOI EuDML