Journal article 552 views 104 downloads
Invariant probability measures for path-dependent random diffusions
Jianhai Bao,
Jinghai Shao,
Chenggui Yuan 
Nonlinear Analysis, Volume: 228, Start page: 113201
Swansea University Author:
Chenggui Yuan
DOI (Published version): 10.1016/j.na.2022.113201
Abstract
In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, we show that the path-dependent random diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also,...
| Published in: | Nonlinear Analysis |
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| ISSN: | 0362-546X |
| Published: |
Elsevier BV
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa62231 |
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| Abstract: |
In this work, we are concerned with path-dependent random diffusions. Under certain ergodic condition, we show that the path-dependent random diffusion under consideration has a unique invariant probability measure and converges exponentially to its equilibrium under the Wasserstein distance. Also, we demonstrate that the time discretization of the path-dependent random diffusion involved admits a unique (numerical) invariant probability measure and preserves the corresponding ergodic property when the step size is sufficiently small. Moreover, we provide an estimate on the exponential functional of the discrete observation for a Markov chain, which may be interesting by itself. |
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| Keywords: |
Invariant probability measure; Path-dependent random diffusion; Ergodicity; Wasserstein distance; Euler–Maruyama scheme |
| College: |
Faculty of Science and Engineering |
| Start Page: |
113201 |