The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 4 Issue 1
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- Pages.47-60
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- 1997
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION
- Chang, Seung-Jun (Department of Mathematics, Dankook University) ;
- Lee, Sang-Deok (Department of Mathematics, Dankook University)
- Published : 1997.06.01
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