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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Stochastic control based on time-change transformations for stochastic processes with Lévy noise


Authors: S. V. Bodnarchuk and O. M. Kulik
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 13-31
MSC (2010): Primary 60H07; Secondary 60G51
Published electronically: August 20, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We propose a new method of stochastic control for stochastic processes with Lévy noise based on time-change transformations. Applying this method, we prove that the integral minorization condition holds for Markov processes defined by stochastic equations with Lévy noise and obtain the explicit estimates for the rate of convergence in the ergodic theorem.


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Additional Information

S. V. Bodnarchuk
Affiliation: National Technical University of Ukraine “KPI”, Peremogy Avenue 37, 03056, Kyiv, Ukraine
Email: sem{\textunderscore}bodn@ukr.net

O. M. Kulik
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs′ka Street 3, 01601, Kyiv, Ukraine
Email: kulik@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00886-2
PII: S 0094-9000(2013)00886-2
Keywords: L\'evy process, stochastic equation, stochastic control, time-change transformations
Received by editor(s): December 5, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society