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Diffusions as a limit of stretched Brownian motions. (English) Zbl 0542.60079

The authors show that any regular diffusion on the line can be written as a weak limit of a class of processes called stretched Brownian motions. These are diffusions whose scale functions are piecewise-linear and whose speed measures have densities which are step-functions. The canonical example of such a process is the skew Brownian motion described in the book of K. Itô and H. P. McKean, Diffusion processes and their sample paths. (1965; Zbl 0127.095), 2nd corrected printing 1974. The stretched Brownian motions are in turn shown to be weak limits of certain random walks.
Reviewer: J.Walsh

MSC:

60J60 Diffusion processes
60J65 Brownian motion

Citations:

Zbl 0127.095
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References:

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