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Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales

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  • Wenqing Hu

Abstract

We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale ( -time scale).

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  • Wenqing Hu, 2017. "Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2017, pages 1-13, April.
    • Handle: RePEc:hin:jnlaaa:9140138
    DOI: 10.1155/2017/9140138
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    Cited by:

    1. Dhama, Soniya & Abbas, Syed & Debbouche, Amar, 2020. "Doubly-weighted pseudo almost automorphic solutions for stochastic dynamic equations with Stepanov-like coefficients on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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