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 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.
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
Mathematics and Statistics
Keywords and Phrases
Bochner integral; Random differential equations; Random process; Time scales
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2022