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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 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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