Name
Title | ||
|---|---|---|
Linear Control Systems on Unbounded Time Intervals and Invariant Measures of Ornstein--Uhlenbeck Processes in Hilbert Spaces |
Abstract | ||
|---|---|---|
We consider linear control systems in a Hilbert space over an unbounded time interval of the form $$ y_\alpha'(t)=(A-\alpha I)y_\alpha(t)+Bu(t), \qquad t\in (-\infty, T], $$ with bounded control operator B, under appropriate stability assumptions on the operator A. We study how the space of states reachable at time T depends on the parameter $\alpha\geq 0$. We apply the results to study the dependence on $\alpha$ of the Cameron--Martin spaces of the invariant measures of the Ornstein--Uhlenbeck processes $X_\alpha$ defined by the equation driven by the Wiener process W: $$ dX_\alpha(t) = (A-\alpha I) X_\alpha(t)\; dt + B\; dW(t),\qquad t\geq 0. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1137/S0363012902414652 | SIAM J. Control and Optimization |
Keywords | Field | DocType |
hilbert space,linear control systems,unbounded time intervals,invariant measure,unbounded time interval,bounded control operator b,invariant measures,martin space,uhlenbeck processes,infinite dimensional control systems,hilbert spaces,reachability,states reachable,ornstein-uhlenbeck process,appropriate stability assumption,linear control system,wiener process,control system,ornstein uhlenbeck process | Wiener process,Hilbert space,Bounded operator,Linear system,Mathematical analysis,Reachability,Invariant (mathematics),Ornstein–Uhlenbeck process,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
42 | 5 | 0363-0129 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Fuhrman | 1 | 24 | 7.45 |
| Anna Maria Paganoni | 2 | 7 | 4.45 |