Lagrangian for pinned diffusion process

Keisuke Hara and Yoichiro Takahashi
Additional contact information
Keisuke Hara: University of Tokyo, Graduate School of Mathematical Sciences
Yoichiro Takahashi: Kyoto University, Research Institute for Mathematical Science

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 117-128 from Springer

Abstract: Abstract In the 1960s Professor K. Itô tried to understand the Feynman path integral probabilistically and constructed its integral representation over time dependent Hilbert spaces ([11], also [10]). Near the end of the 1970s D.Fujiwara succeeded in proving the existence of the limit of finite dimensional path integrals for Schrödinger equations in a very strong sense [3], and later in showing “Itô’s version” [4]. Inspired by their works and looking at the discussions on the effect of curvature among physicists, one of the authors started studying the problem of most probable path or the Lagrangian or the Onsager-Machlup function or the probability functional for diffusion process on manifolds (cf., e.g., [5],[16]), and which is completely determined by a collaboration with S. Watanabe [18] (see Theorem 1.2 below).

Keywords: Stochastic Differential Equation; Ergodic Theorem; Radial Motion; Tubular Neighborhood; Radial Part (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68532-6_7

Ordering information: This item can be ordered from
http://www.springer.com/9784431685326

DOI: 10.1007/978-4-431-68532-6_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().