Hilbert-space-valued super-Brownian motion and related evolution equations

Authors
Kallianpur, G Sundar, P
Citation
G. Kallianpur et P. Sundar, Hilbert-space-valued super-Brownian motion and related evolution equations, APPL MATH O, 41(1), 2000, pp. 141-154
Citations number
11
Categorie Soggetti
Mathematics
Journal title
APPLIED MATHEMATICS AND OPTIMIZATION
ISSN journal
00954616 → ACNP
Volume
41
Issue
1
Year of publication
2000
Pages
141 - 154
Database
ISI
SICI code
0095-4616(200001/02)41:1<141:HSMARE>2.0.ZU;2-S
Abstract
A stochastic partial differential equation in which the square root of the solution appears as the diffusion coefficient is studied as a particular ca se of stochastic evolution equations. Weak existence of a solution is prove d by the Euler approximation scheme. The super-Brownian motion on [0,1] is also studied as a Hilbert-space-valued equation. In this set up, weak exist ence, pathwise uniqueness, and positivity of solutions are obtained in any dimension d.