Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 57, pp. 1-15.

Title: Stochastic dynamic equations on general time scales
        
Authors: Martin Bohner (Missouri Univ. of Science and Tech., Rolla, MO, USA)
         Olexandr M. Stanzhytskyi (Taras Shevchenko National Univ., Kiev, Ukraina)
         Anastasiia O. Bratochkina (Taras Shevchenko National Univ., Kiev, Ukraina)

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.