Introduction to stochastic partial differential equations. (English) Zbl 1253.60001
Ekhaguere, G. O. S. (ed.) et al., New directions in the mathematical and computer sciences. Selected papers from the 4th international workshop and conference, Abuja, Nigeria, October 8–13, 2007. Lagos: International Centre for Mathematical & Computer Sciences (ICMCS) (ISBN 978-37246-3-0/pbk). Publications of the ICMCS 4, 159-232 (2008).
Summary: We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of Itô type. This is then used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochastic evolution problems in Hilbert space. Finally, this abstract theory is applied to the linear heat and wave equations driven by additive noise.
For the entire collection see [Zbl 1245.00041].
For the entire collection see [Zbl 1245.00041].
MSC:
| 60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
