Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2006; 43(3): 461-489

Printed May 1, 2006

Copyright © The Korean Mathematical Society.

The measure-valued Dyson series and its stability theorem

Kun Sik Ryu and Man Kyu Im

Han Nam University, Han Nam University

Abstract

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

Keywords: analogue of Wiener measure, Bartle integral, Dyson series, measure-valued Feynman-Kac formula, Volterra integral equation, stability theorem

MSC numbers: Primary 28C35, 28C20, 45D05, 47A56