Martin Bohner, Olexandr M. Stanzhytskyi, Anastasiia O. Bratochkina
Abstract:
In this article, we construct stochastic integral and
stochastic differential equations on general time scales.
We call these equations stochastic dynamic equations.
We provide the existence and uniqueness theorem for solutions
of stochastic dynamic equations.
The crucial tool of our construction is a result about
a connection between the time scales Lebesgue integral and
the Lebesgue integral in the common sense.
Submitted October 25, 2012. Published February 26, 2013.
Math Subject Classifications: 34N05, 60H10, 60H05, 6530, 26E70, 39A12, 39A10.
Key Words: Time scale; stochastic integral; stochastic dynamic equation;
time scales integral; Markov process.
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Martin Bohner Missouri University of Science and Technology Rolla, MO 65409-0020, USA email: bohner@mst.edu |
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Olexandr M. Stanzhytskyi Taras Shevchenko National University of Kiev Kiev, Ukraina email: ostanzh@gmail.com |
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Anastasiia O. Bratochkina Taras Shevchenko National University of Kiev Kiev, Ukraina email: sestri4kina@ukr.net |
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