Abstract
One considers a certain characteristic, similar to the quadratic variation, of processes with independent increments. One investigates its almost surely behavior as t→∞.
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Literature cited
V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, New York (1975).
A. A. 'Borovkov, “On the rate of convergence in the invariance principle,” Teor. Veroyatn. Primen.,18, No. 2, 217–234 (1973).
I. I. Gikhman (Gihman) and A. V. Skorokhod (Skorohod), The Theory of Stochastic Processes, Vol. I, Springer-Verlag, New York (1974).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 78–88, 1983.
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Egorov, V.A. Asymptotic behavior of the quadratic variation for trajectories of processes with independent increments. J Math Sci 27, 3219–3226 (1984). https://doi.org/10.1007/BF01850669
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DOI: https://doi.org/10.1007/BF01850669