Integrated solutions of stochastic evolution equations with additive noise (Q2758191)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Integrated solutions of stochastic evolution equations with additive noise |
scientific article; zbMATH DE number 1679525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integrated solutions of stochastic evolution equations with additive noise |
scientific article; zbMATH DE number 1679525 |
Statements
Integrated solutions of stochastic evolution equations with additive noise (English)
0 references
25 November 2002
0 references
stochastic differential equation
0 references
Cauchy problem
0 references
existence
0 references
stochastic wave equation
0 references
The abstract stochastic evolution equation \(dX(t)=AX(t) dt + B dW(t)\), \(X(0)=\xi\), is investigated, where \(A\) is a generator of an \(n\)-times integrated semigroup on a Hilbert space. The existence of a weak \(n\)-integrated solution is established and the existence of a continuous solution is discussed. Finally, the results are applied to a stochastic wave equation.
0 references
