Stochastic dynamic equations on general time scales

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.

Keywords

• Time scale
• stochastic integral
• stochastic dynamic equation
• time scales integral
• Markov process