On Itô's formula for elliptic diffusion processes

Xavier Bardina, Carles Rovira

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

Abstract

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Itô's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x. © 2007 ISI/BS.
Original languageEnglish
Pages (from-to)820-830
JournalBernoulli
Volume13
DOIs
Publication statusPublished - 1 Dec 2007

Keywords

  • Diffusion processes
  • Integration with respect to local time
  • Itô's formula
  • Local time

Fingerprint

Dive into the research topics of 'On Itô's formula for elliptic diffusion processes'. Together they form a unique fingerprint.

Cite this