Diffusion and Deterministic Systems
Institute of Mathematics, University of Silesia,
Corresponding author. E-mail: firstname.lastname@example.org
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
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