Vector-Valued Functions on Time Scales and Random Differential Equations

Abstract

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 Lp-calculus for random processes on time scales, and present some results concerning the sample path and Lebesgue and Lp-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 Lp-calculus. An existence result is considered which gives sufficient conditions under which a sample path solution is also an Lp-solution.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Bochner Integral; Random Differential Equations; Random Process; Time Scales

International Standard Serial Number (ISSN)

1807-0302; 2238-3603

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2022 Springer, All rights reserved.

Publication Date

01 Jun 2022

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