Hamzi - Eurandom

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$Continuous-time random walks, fractional calculus and ... - Eurandom$

Nonlinear SDEs in RKHSes • Assumption2: The measure P∞ is the invariant measure of the OU process and P∞ is the pushforward along Φ of the unknown invariant measure µ∞ on the statespace X we would like to approximate. • Assumption3: The measure µ∞ is absolutely continuous with respect to Lebesgue measure, and so admits a density. . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 46 / 55
Nonlinear SDEs in RKHSes • The stationary measure µ∞ is defined on a finite dimensional space, so together with part (iii) of Assumption A, we may consider the corresponding density ρ∞(x) ∝ exp ( − ˆ Lc(x)) . . . . . . Boumediene <strong>Hamzi</strong> (Imperial College) On Control and RDS in RKHS June 4th, 2012 47 / 55
Page 1 and 2: Preliminary Results on Control and
Page 3 and 4: Outline • Review of Some Concepts
Page 5 and 6: Review of Some Concepts for Linear
Page 11 and 12: Controllability and Observability E
Page 13 and 14: Balancing of Linear Control Systems
Page 15 and 16: Balancing of Nonlinear Systems •
Page 17 and 18: Empirical Estimates of the Gramians
Page 19 and 20: Reproducing Kernel Hilbert Spaces
Page 21 and 22: Reproducing Kernel Hilbert Spaces T
Page 33 and 34: Balanced Reduction of Nonlinear Con
Page 35 and 36: Balancing in RKHS • “Balancing
Page 37 and 38: Experiment: Inputs ◮ Excite with
Page 39 and 40: Experiment diag(TKcT T ) 10 −1 10
Page 45: Nonlinear SDEs in RKHSes • Assump
Page 49 and 50: Parameter Estimation for SDEs • I
Page 51 and 52: Parameter Estimation for SDEs • I
Page 53 and 54: Example (A Fokker-Planck Integrable
Page 55: Open Questions • Derivation of da

Hamzi - Eurandom

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