Electron. J. Diff. Equ., Vol. 2013 (2013), No. 57, pp. 1-15.

Stochastic dynamic equations on general time scales

Martin Bohner, Olexandr M. Stanzhytskyi, Anastasiia O. Bratochkina

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
Olexandr M. Stanzhytskyi
Taras Shevchenko National University of Kiev
Kiev, Ukraina
email: ostanzh@gmail.com
Anastasiia O. Bratochkina
Taras Shevchenko National University of Kiev
Kiev, Ukraina
email: sestri4kina@ukr.net

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