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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conditions for the absolute continuity of two diffusions


Author: Steven Orey
Journal: Trans. Amer. Math. Soc. 193 (1974), 413-426
MSC: Primary 60J60
DOI: https://doi.org/10.1090/S0002-9947-1974-0370794-1
MathSciNet review: 0370794
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Abstract: Consider two diffusion processes on the line. For each starting point x and each finite time t, consider the measures these processes induce in the space of continuous functions on [0, t]. Necessary and sufficient conditions on the generators are found for the induced measures to be mutually absolutely continuous for each x and t. If the first process is Brownian motion, the second one must be Brownian motion with drift $ b(x)$, where $ b(x)$ is locally in $ {L_2}$ and satisfies a certain growth condition at $ \pm \infty $.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0370794-1
Article copyright: © Copyright 1974 American Mathematical Society