Geodesic
Energy saving approximation of Wiener process under unilateral constraints
Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 1, pp. 76-90

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We consider an energy saving approximation of a Wiener process under unilateral constraints. We show that, almost surely, on large time intervals the minimal energy necessary for the approximation logarithmically depends on the interval length. We also construct an adaptive approximation strategy optimal in a class of diffusion strategies and providing the logarithmic order of energy consumption.
Keywords: Wiener process, Markovian pursuit strategy
Mots-clés : concave majorant. 
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     author = {M. A. Lifshits and S. E. Nikitin},
     title = {Energy saving approximation of {Wiener} process under unilateral constraints},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {76--90},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2024_69_1_a3/}
}
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M. A. Lifshits; S. E. Nikitin. Energy saving approximation of Wiener process under unilateral constraints. Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 1, pp. 76-90. http://geodesic.mathdoc.fr/item/TVP_2024_69_1_a3/