| Issue |
ESAIM: PS
Volume 28, 2024
|
|
|---|---|---|
| Page(s) | 75 - 109 | |
| DOI | https://doi.org/10.1051/ps/2024004 | |
| Published online | 04 April 2024 | |
Splitting for some classes of homeomorphic and coalescing stochastic flows
Institute of Mathematics, National Academy of Sciences of Ukraine,
Tereshchenkivska Str. 3,
Kyiv
01601,
Ukraine
* Corresponding author: vovchansky.m@gmail.com
Received:
2
May
2023
Accepted:
4
March
2024
The splitting scheme (the Kato-Trotter formula) is applied to stochastic flows with common noise of the type introduced by Th.E. Harris. The case of possibly coalescing flows with continuous infinitesimal covariance is considered and the weak convergence of the corresponding finite-dimensional motions is established. As applications, results for the convergence of the associated pushforward measures and dual flows are given. Similarities between splitting and the Euler-Maruyama scheme yield estimates of the speed of the convergence under additional regularity assumptions.
Mathematics Subject Classification: 60H35 / 60K35 / 65C30
Key words: Splitting scheme / stochastic flow / stochastic differential equation
© The authors. Published by EDP Sciences, SMAI 2024
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