Abstract:We study the asymptotic behavior as t → ∞ of a time-dependent family (µt) t≥0 of probability measures on R solving the kinetic-type evolution equation ∂tµt + µt = Q(µt) where Q is a smoothing transformation on R. This problem has been investigated earlier, e.g. by Bassetti and Ladelli [Ann. Appl. Probab. 22(5): 1928-1961, 2012 and Bogus, Buraczewski and Marynych [To appear in Stochastic Process. Appl.]. Combining the refined analysis of the latter paper providing a probabilistic description of the solution µt… Show more
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