Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T11:35:00.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Construction of a solution of a certain evolution equation

Published online by Cambridge University Press:  22 January 2016

Akinobu Shimizu
Akinobu Shimizu*
Affiliation:
Nagoya Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let us consider the stochastic differential equation,

with initial condition,

where Bt, t ≧ 0,is a one-dimensional Brownian motion, and Lx is a second order uniformly elliptic partial differential operator satisfying some additional conditions that will be described in §2. The existence and the uniqueness of solutions of the Cauchy problem have been established by B. L. Rozovskii [8].

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977, pp. 23 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Balakrishnan, A. V.; Stochastic bilinear partial differential equations, the U.S.Italy conference on variable structure systems, Oregon, May, 1974.Google Scholar
[2] Dawson, D. A.; Stochastic evolution equations and related measure processes, J. Multivariate anal., Vol. 5, No. 1 (1975).Google Scholar
[3] Eidel’man, S. D.; Parabolic systems, Moscow, 1964.Google Scholar
[4] Fleming, W. H.; Distributed parameter stochastic systems in population biology, m.s., Brown University, Providence, R. I. Google Scholar
[5] Hida, T. and Ikeda, N.; Analysis on Hilbert space with reproducing kernel arising from multiple Wiener integral, Proc. Fifth Berkeley Symp. on math. Statist, and Probability, Vol. 2, Part 1 (1967), 117–143.Google Scholar
[6] Hida, T.; Brownian motion (in Japanese), Iwanami Pub. Co., 1975.Google Scholar
[7] Hida, T.; Analysis of Brownian functionals, Carleton University lecture notes, 1975.Google Scholar
[8] Rozovskii, B. L.; On stochastic differential equations with partial derivatives (in Russian), Math. Sb., Vol. 06 (138), No. 2 (1975), 314–341.Google Scholar