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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.4 No.1

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THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.1, pp.47-60
Chang, Seung-Jun (Department of Mathematics, Dankook University)
Lee, Sang-Deok (Department of Mathematics, Dankook University)
Chang, Seung-Jun, & Lee, Sang-Deok. (1997). THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION. 한국수학교육학회지시리즈B:순수및응용수학, 4(1), 47-60.

Abstract

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

keywords
Generalized Brownian motion process, Function space integral, Coditional function space integral, Kac-Feynman integral equation

한국수학교육학회지시리즈B:순수및응용수학

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