Stochastic evolution equations with Volterra noise
| Autor: | Petr Čoupek, Bohdan Maslowski |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Fractional Brownian motion Covariance function Stochastic process Applied Mathematics 010102 general mathematics Mathematical analysis Hilbert space 01 natural sciences Noise (electronics) Volterra integral equation 010104 statistics & probability symbols.namesake Square-integrable function Modeling and Simulation Kernel (statistics) symbols 0101 mathematics Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 127:877-900 |
| ISSN: | 0304-4149 |
| Popis: | Volterra processes are continuous stochastic processes whose covariance function can be written in the form R ( s , t ) = ∫ 0 s ∧ t K ( s , r ) K ( t , r ) d r , where K is a suitable square integrable kernel. Examples of such processes are the fractional Brownian motion, multifractional Brownian motion or (in the non-Gaussian case) Rosenblatt process. In the first part, stochastic integral with respect to Volterra processes and cylindrical Volterra process in Hilbert spaces are defined and some of their properties are studied. In the second part, these results are applied to linear stochastic equations in Hilbert spaces driven by cylindrical Volterra processes. Measurability, mean-square continuity and paths continuity of their solutions are proved under various sets of conditions. The general results are illustrated by examples of parabolic and hyperbolic SPDEs. |
| Databáze: | OpenAIRE |
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