Abstract
We investigate properties of a solution of a stochastic differential equation with interaction and their dependence on a space variable. It is shown that x(u, t) − u belongs to S under certain conditions imposed on the coefficients, and, furthermore, it depends continuously on the initial measure as an element of S. We also study the problem of the existence of a solution of the equation governed by a generalized function.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1020 – 1029, August, 2005.
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Karlikova, M.P. On the Transfer of Generalized Functions by an Evolution Flow. Ukr Math J 57, 1201–1213 (2005). https://doi.org/10.1007/s11253-005-0257-9
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DOI: https://doi.org/10.1007/s11253-005-0257-9