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 Verlag, 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
© 2022 Springer, All rights reserved.
Publication Date
01 Jun 2022
