| Title:
|
Periodic and almost periodic flows of periodic Ito equations (English) |
| Author:
|
Tudor, C. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
225-238 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the $l^p$-bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established. (English) |
| Keyword:
|
trajectory of an almost periodic flow |
| Keyword:
|
uniform asymptotic stability |
| Keyword:
|
Itô equations |
| Keyword:
|
periodic and almost periodic flows |
| Keyword:
|
asymptotically almost periodic solution |
| MSC:
|
46N30 |
| MSC:
|
60B10 |
| MSC:
|
60H10 |
| MSC:
|
60H20 |
| idZBL:
|
Zbl 0765.60059 |
| idMR:
|
MR1184536 |
| DOI:
|
10.21136/MB.1992.126284 |
| . |
| Date available:
|
2009-09-24T20:52:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126284 |
| . |
| Reference:
|
[1] A. Halanay T. Morozan, C. Tudor: Bounded solutions of affine stochastic differential equations and stability.Časopis pro pěstování matematiky 111 (1986), 127-136. MR 0847312 |
| Reference:
|
[2] A. Halanay T. Morozan, C. Tudor: Tracking almost periodic signals white noise perturbations.Stochastics 21 (1987), 287-301. MR 0905050, 10.1080/17442508708833461 |
| Reference:
|
[3] A. Haraux: A simple almost-periodicity criterion and applications.J. Differential Equations 66 (1987), 51-61. Zbl 0608.34049, MR 0871570, 10.1016/0022-0396(87)90039-8 |
| Reference:
|
[4] N. Ikeda, S. Watanabe: Stochastic Differential Equations and Diffusion Processes.North Holland, 1981. Zbl 0495.60005, MR 1011252 |
| Reference:
|
[5] R. Khasminskii: Stability of Differential Equations under Random Perturbations.Nauka, 1969. (In russian.) |
| Reference:
|
[6] Y. Miyahara: Ultimate boundedness of the systems governed by stochastic differential equations.Nagoya Math. J. 47 (1972), 111-144. Zbl 0222.60036, MR 0319269, 10.1017/S0027763000014951 |
| Reference:
|
[7] T. Morozan: Bounded and periodic solutions of affine stochastic differential equations.Studii si Cercetari Matematice 38 (1986), 523-527. Zbl 0623.60075, MR 0878757 |
| Reference:
|
[8] W. Römisch, A. Wakolbinger: On convergence rates of approximate solutions of stochastic equations.Lect. Notes in Control and Information Sciences 96, Springer-Verlag, 1986. |
| Reference:
|
[9] A. Skorokhod: Studies in the Theory of Random Processes.Addison-Wesley, 1965. Zbl 0146.37701, MR 0185620 |
| Reference:
|
[10] D. V. Stroock, S. R. Varadhan: Multidimensional Diffusion Processes.Springer-Verlag, 1979. Zbl 0426.60069, MR 0532498 |
| Reference:
|
[11] C. Tudor: On Volterra equations driven by semimartingales.J. Differential Equations 72 no. 2 (1988), 200-217. Zbl 0649.60072, MR 0952895, 10.1016/0022-0396(88)90002-2 |
| Reference:
|
[12] C. Vârsan: Asymptotic almost periodic solutions for stochastic differential equations.Tôhoku Math. J. 41 no. 4 (1989), 609-618. MR 1025326, 10.2748/tmj/1178227731 |
| . |
