Stochastic evolution equations in UMD Banach spaces
| dc.creator | van Neerven, J. M. A. M. | |
| dc.creator | Veraar, M. C. | |
| dc.creator | Weis, L. | |
| dc.date | 2008-04-06 | |
| dc.date.accessioned | 2026-07-07T09:30:45Z | |
| dc.date.available | 2026-07-07T09:30:45Z | |
| dc.description | We discuss existence, uniqueness, and space-time Hölder regularity for solutions of the parabolic stochastic evolution equation dU(t) = (AU(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), t\in [0,\Tend], U(0) = u_0, where $A$ generates an analytic $C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical Brownian motion with values in a Hilbert space $H$. We prove that if the mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$ satisfy suitable Lipschitz conditions and $u_0$ is $\F_0$-measurable and bounded, then this problem has a unique mild solution, which has trajectories in $C^ł([0,T];\D((-A)^θ)$ provided $λ\ge 0$ and $θ\ge 0$ satisfy $ł+θ<\frac12$. Various extensions of this result are given and the results are applied to parabolic stochastic partial differential equations. | |
| dc.description | Accepted for publication in Journal of Functional Analysis | |
| dc.identifier | https://arxiv.org/abs/0804.0932 | |
| dc.identifier | http://arxiv.org/abs/0804.0932 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158219 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 47D06; 60H15; 28C20; 46B09 | |
| dc.title | Stochastic evolution equations in UMD Banach spaces | |
| dc.type | text |