Mixed stochastic delay differential equations

Shevchenko, G.

doi:10.1090/S0094-9000-2015-00944-3

Mixed stochastic delay differential equations

Author: G. Shevchenko
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
MathSciNet review: 3235184
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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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