Abstract
A one-dimensional evolution equation transformable into a linear one coupled to a quadratic Smoluchowski (an Ornstein-Uhlenbeck) noise is considered. A one-dimensional probability distribution is obtained by way of a characteristic function which is expressed by functionals of the Smoluchowski process. It is shown that in the frame of the presented approach the probability density can be found only for a particular value of the damping constant in the linear-type relaxation equation. It is also shown that in a special case the white noise limit may be performed.
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Supported in part by the Polish Academy of Sciences under Contract No. MR 1-9.
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Łuczka, J. Exact probability distribution for soluble model with quadratic noise. J Stat Phys 42, 1009–1018 (1986). https://doi.org/10.1007/BF01010459
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DOI: https://doi.org/10.1007/BF01010459