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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: 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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  • 1. Alexey M. Kulik, Exponential ergodicity of the solutions to SDE’s with a jump noise, Stochastic Process. Appl. 119 (2009), no. 2, 602–632. MR 2494006, 10.1016/
  • 2. Alexey M. Kulik, Absolute continuity and convergence in variation for distributions of functionals of Poisson point measure, J. Theoret. Probab. 24 (2011), no. 1, 1–38. MR 2782709, 10.1007/s10959-010-0325-4
  • 3. Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
  • 4. R. L. Dobrušin, Definition of a system of random variables by means of conditional distributions, Teor. Verojatnost. i Primenen. 15 (1970), 469–497 (Russian, with English summary). MR 0298716
  • 5. A. Yu. Veretennikov, Coupling method for Markov chains under integral Doeblin type condition, Proceedings of the Conference Dedicated to the 90th Anniversary of Boris Vladimirovich Gnedenko (Kyiv, 2002), 2002, pp. 383–390. MR 2027410
  • 6. L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute of Mathematical Sciences, New York University, New York, 1974. With a chapter by E. Zehnder; Notes by R. A. Artino; Lecture Notes, 1973–1974. MR 0488102
  • 7. Peter Lancaster, Theory of matrices, Academic Press, New York-London, 1969. MR 0245579

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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}

O. M. Kulik
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs′ka Street 3, 01601, Kyiv, Ukraine

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