Abstract
In the paper one investigates the behavior of sequences of trajectories of step-like random processes, considered as random sets in the plane. One obtains results on the asymptotic behavior of processes, inaccessible by the classical approach. The description of the class of limit distributions is also given.
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Literature cited
G. Matheron, Random Sets and Integral Geometry, Wiley, New York (1975).
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 122–129, 1983.
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Lyashenko, N.N. Weak convergence of step processes in the space of closed sets. J Math Sci 27, 3251–3257 (1984). https://doi.org/10.1007/BF01850673
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DOI: https://doi.org/10.1007/BF01850673