Abstract
The properties of a linear differential equation with an additive quadratic noise are analyzed. The graphs of the probability distribution of the process are presented for various values of the noise strength and the damping constant. The time evolution of the distribution is also shown. An infinitesimal generator of the evolution operator of the process is constructed. A diffusion-type approximation is considered and a comparison of the exact solution with the approximate solution is carried out.
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This paper is dedicated to the memory of Prof. A. Pawlikowski.
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Łuczka, J. Relaxation problem with a quadratic noise: Analysis. J Stat Phys 47, 505–526 (1987). https://doi.org/10.1007/BF01007523
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DOI: https://doi.org/10.1007/BF01007523