| Title:
|
Asymptotic stability condition for stochastic Markovian systems of differential equations (English) |
| Author:
|
Shmerling, Efraim |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
443-448 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by ${\rm d} X(t) = A(\xi (t))X(t) {\rm d} t + H(\xi (t))X(t) {\rm d} w(t)$, where $\xi (t)$ is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition. (English) |
| Keyword:
|
jump parameter system |
| Keyword:
|
Markov process |
| Keyword:
|
asymptotic stability |
| MSC:
|
34F05 |
| MSC:
|
47B80 |
| MSC:
|
60H25 |
| MSC:
|
93E03 |
| idZBL:
|
Zbl 1224.34182 |
| idMR:
|
MR2681017 |
| DOI:
|
10.21136/MB.2010.140834 |
| . |
| Date available:
|
2010-11-24T08:30:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140834 |
| . |
| Reference:
|
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| . |
