Abstract
In the paper one considers random processes ξs o⩽s⩽t with independent increments, continuous in the mean (∀P<∞). One establishes relations among multiple integrals, variations, i.e., the limits of sums of the form\(\sum {\left( {\xi _{t_i } - \xi _{t_{i - 1} } } \right)^n } \), and the Itô stochastic integrals.
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Literature cited
Yu. M. Kabanov and A. V. Skorokhod, “Extended stochastic integrals,” in: Proc. School and Seminar on the Theory of Random Processes (Drushkininkai, 1974), Part I, Inst. Fiz. i Mat. Akad. Nauk LitSSR, Vilnius (1975), pp. 123–167.
H. P. McKean, Jr., Stochastic Integrals, Academic Press, New York (1969).
A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Nauka, Moscow (1964).
E. Lukacs, Characteristic Functions, Hafner, New York (1970).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskago Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 25–35, 1983.
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Bobkov, S.G. Variations of random processes with independent increments. J Math Sci 27, 3181–3189 (1984). https://doi.org/10.1007/BF01850664
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DOI: https://doi.org/10.1007/BF01850664