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Vector-valued functions on time scales and random differential equations

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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.

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The authors would like to thank both referees for carefully reading this manuscript and making many important suggestions, leading to a better presentation of the results.

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Correspondence to Vasile Lupulescu.

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Communicated by Juan Carlos Cortes.

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Bohner, M., Lupulescu, V., O’Regan, D. et al. Vector-valued functions on time scales and random differential equations. Comp. Appl. Math. 41, 153 (2022).

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