Vector-valued functions on time scales and random differential equations

In this article, we first present the construction and basic properties of the Bochner integral for vector-valued functions on an arbitrary time scale. Using the properties of the Bochner integral, we develop an L^p-calculus for random processes on time scales, and present some results concerning the sample path and Lebesgue and L^p-integrability of a random process on time scales. Finally, we study random differential equations on time scales in the framework of the pth moment or L^p-calculus. An existence result is considered which gives sufficient conditions under which a sample path solution is also an L^p-solution.