Abstract
We develop simple rigorous techniques to estimate the behavior of general one-dimensional diffusion processes. Any one-dimensional diffusion process (with drift) can be mapped onto a symmetric diffusion through an explicit change of variable. For such processes we can estimate explicitly the diffusion exponent, the recurrence properties, and the large fluctuations. In a second part, we apply these results to different models (including the Sinaï random walk: diffusion in a random drift) and we show how the main features of the diffusion can be readily handled.
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Delyon, F., Luciani, JF. Behavior of general one-dimensional diffusion processes. J Stat Phys 54, 1065–1080 (1989). https://doi.org/10.1007/BF01019787
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DOI: https://doi.org/10.1007/BF01019787