Name
Abstract | ||
|---|---|---|
Recent work on singular perturbation solutions that persist in the presence of noise is described. Two different settings are considered: small deviation theory in quasi-static problems, where there are small amplitude but highly irregular perturbations, and averaging problems where there are ergodic stochastic perturbations. In the first case, it is shown that quasi-static approx imations can be valid when the underlying problem experiences small deviation perturbations in problems that are stable under persistent disturbances. In the second, averaging principles are described for certain dynamical systems in Hilbert spaces that include applications to a wide variety of initial-boundary value problems for partial differential equations and for Volterra integral equations. These methods are applied here to four problems arising in applications. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1137/S0036139993269229 | SIAM Journal of Applied Mathematics |
Keywords | Field | DocType |
noisy system,singular perturbation solution,singular perturbation | Hilbert space,Mathematical optimization,Mathematical analysis,Ergodic theory,Integral equation,Singular perturbation,Dynamical systems theory,Partial differential equation,Mathematics,Dynamical system,Volterra integral equation | Journal |
Volume | Issue | ISSN |
55 | 2 | 0036-1399 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Frank C. Hoppensteadt | 1 | 60 | 21.43 |