Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
|
|
---|---|---|
Page(s) | 139 - 150 | |
DOI | https://doi.org/10.1051/mmnp/20149110 | |
Published online | 07 February 2014 |
Diffusion and Deterministic Systems
Institute of Mathematics, University of Silesia,
Bankowa 14,
40-007
Katowice,
Poland
⋆
Corresponding author. E-mail: mtyran@us.edu.pl
We show that simple diffusion processes are weak limits of piecewise continuous processes constructed within a totally deterministic framework. The proofs are based on the continuous mapping theorem and the functional central limit theorem.
Mathematics Subject Classification: 28D05 / 37A50 / 60F17 / 60G51 / 60J60
Key words: functional limit theorem / piecewise monotonic maps / Ornstein-Uhlenbeck process / Langevin equation / diffusion
© EDP Sciences, 2014
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