For a standard Wiener process on a certain probability space we consider the family of all probability measures on the same space such that each one is a result of Girsanov’s change of the original measure. The one of those measures that maximizes the local time at zero (properly normalized) of the corresponding process is constructed in this paper. That process turns out to be a non-Markovian one. To compare the optimal process with others, we evaluate the values of the payoff functions for some Markov processes of the type. Bibliography: 3 titles.
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E. B. Dynkin, Markov processes [in Russian], Fizmatgiz, Moscow (1963); English transl.: Academic Press, New York etc. (1965).
R. Sh. Liptser and A. N. Shiryaev, Statistics of Random Processes [in Russian], Nauka, Moscow (1974); English transl.: Springer, Berlin (1977).
M. M. Osypchuk and M. I. Portenko, “On Ornstein–Uhlenbeck’s measure of a Hilbertian ball in the space of continuous functions” [in Ukrainian], In: Mathematics Today ’10’ Osvita Ukrainy, Kyiv (2011).
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Dedicated to N. V. Krylov whose contribution into modern mathematics is impressive
Translated from Problems in Mathematical Analysis 61, October 2011, pp. 139–146.
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Osypchuk, M.M., Portenko, M.I. An extremum problem for some class of Brownian motions with drifts. J Math Sci 179, 164–173 (2011). https://doi.org/10.1007/s10958-011-0587-0
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DOI: https://doi.org/10.1007/s10958-011-0587-0