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.
Recommended Citation
M. Bohner et al., "Vector-Valued Functions on Time Scales and Random Differential Equations," Computational and Applied Mathematics, vol. 41, no. 4, article no. 153, Springer, Jun 2022.
The definitive version is available at https://doi.org/10.1007/s40314-022-01860-z
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
© 2023 Springer, All rights reserved.
Publication Date
01 Jun 2022
