Open Access
January, 2019 Local time penalizations with various clocks for one-dimensional diffusions
Christophe PROFETA, Kouji YANO, Yuko YANO
J. Math. Soc. Japan 71(1): 203-233 (January, 2019). DOI: 10.2969/jmsj/75947594


We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal $\sigma$-finite measures.

Funding Statement

The first and the second authors were supported by JSPS-MAEDI Sakura program. The second author was supported by MEXT KAKENHI grant 26800058, 24540390 and 15H03624. The third author was supported by MEXT KAKENHI grant 23740073.


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Christophe PROFETA. Kouji YANO. Yuko YANO. "Local time penalizations with various clocks for one-dimensional diffusions." J. Math. Soc. Japan 71 (1) 203 - 233, January, 2019.


Received: 30 August 2016; Revised: 13 August 2017; Published: January, 2019
First available in Project Euclid: 5 November 2018

zbMATH: 07056562
MathSciNet: MR3909919
Digital Object Identifier: 10.2969/jmsj/75947594

Primary: 60F05
Secondary: 60G44 , 60J60

Keywords: Excursion measure , Local time , One-dimensional diffusion , Penalization

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 1 • January, 2019
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