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Theory of Probability and Mathematical Statistics

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Mixed stochastic delay differential equations


Author: G. Shevchenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 181-195
MSC (2010): Primary 60H10, 34K50, 60G22
DOI: https://doi.org/10.1090/S0094-9000-2015-00944-3
Published electronically: January 26, 2015
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Abstract: We consider a stochastic delay differential equation driven by a Hölder continuous process $ Z$ and a Wiener process. Under fairly general assumptions on coefficients of the equation, we prove that it has a unique solution. We also give a sufficient condition for finiteness of moments of the solution and prove that the solution depends on $ Z$ continuously.


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Additional Information

G. Shevchenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska, 01601 Kyiv, Ukraine
Email: zhora@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2015-00944-3
Keywords: Fractional Brownian motion, Wiener process, stochastic delay differential equation, mixed stochastic differential equation
Received by editor(s): February 26, 2013
Published electronically: January 26, 2015
Additional Notes: The research was partially supported by the President’s Grant for Young Scientists, Project GP/F49/002
Article copyright: © Copyright 2015 American Mathematical Society