Some variations on Kac's formula for Brownian motion
type: Item
instance of: scholarly article
title: Some variations on Kac's formula for Brownian motion
zbMATH Open document ID: 0678.60075
DOI: 10.1007/BF01051876
author: Dudley Paul Johnson
published in: Journal of Theoretical Probability
publication date: 1989-01-01T00:00:00Z
review text: Let f be a bounded, uniformly continuous function mapping \({\mathbb{R}}^ 4\to {\mathbb{R}}\); let \(\alpha \in C^ 2({\mathbb{R}})\), \(\beta \in C^ 2({\mathbb{R}}^ 3)\), and denote by \(X_ t\) the Brownian motion on \({\mathbb{R}}\). In this short note a generalization of the Feynman-Kac-formula of the form \[ E_ xf\{a+\int^{t}_{0}\beta [b+\int^{s}_{0}\alpha (X_ r)dr,\quad c+s,\quad X_ s]ds,\quad b+\int^{t}_{0}\alpha (X_ s)ds,\quad c+t,\quad X_ t\} \] is considered.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 4111738
zbMATH Keywords: Brownian motion
zbMATH Keywords: generalization of the Feynman-Kac-formula
MaRDI profile type: Publication
cites work: Note on product formulas for operator semigroups
cites work: Q3254057
cites work: Q3721264
cites work: Q5808624
cites work: Feynman Integrals and the Schrödinger Equation
description: scientific article; zbMATH DE number 4111738