| Title:
|
Kolmogorov equation and large-time behaviour for fractional Brownian motion driven linear SDE's (English) |
| Author:
|
Vyoral, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
63-81 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a stochastic process $X_t^x$ which solves an equation \[ {\mathrm d}X_t^x = AX_t^x\mathrm{d}t + \Phi {\mathrm d}B^H_t,\quad X_0^x = x \] where $A$ and $\Phi $ are real matrices and $B^H$ is a fractional Brownian motion with Hurst parameter $H \in (1/2,1)$. The Kolmogorov backward equation for the function $u(t,x) = \mathbb{E} f(X^x_t)$ is derived and exponential convergence of probability distributions of solutions to the limit measure is established. (English) |
| Keyword:
|
fractional Brownian motion |
| Keyword:
|
Kolmogorov backwards equation |
| Keyword:
|
linear stochastic equation |
| MSC:
|
60G15 |
| MSC:
|
60H05 |
| MSC:
|
60H10 |
| idZBL:
|
Zbl 1099.60040 |
| idMR:
|
MR2117696 |
| DOI:
|
10.1007/s10492-005-0004-4 |
| . |
| Date available:
|
2009-09-22T18:20:32Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134590 |
| . |
| Reference:
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