Local time penalizations with various clocks for one-dimensional diffusions

• Profeta Christophe

  Université d'Evry Val-d'Essonne

• Yano Kouji

  Graduate School of Science Kyoto University

• Yano Yuko

  Faculty of Science Kyoto Sangyo University

Abstract

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 𝜎-finite measures.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 71 (1), 203-233, 2019

  The Mathematical Society of Japan

Keywords

• penalization
• one-dimensional diffusion
• local time
• excursion measure

Details

• CRID: 1390282763095331328
• NII Article ID: 130007557117
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/75947594
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 029459895
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I029459895
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed