It\^o's formula, the stochastic exponential and change of measure on general time scales

Wenqing Hu

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arXiv · 1609.05967

It\^o's formula, the stochastic exponential and change of measure on general time scales

Wenqing Hu

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Abstract

We provide an It\^{o}'s formula for stochastic dynamical equation on general time scales. Based on this It\^{o}'s formula we give a closed form expression for stochastic exponential on general time scales. We then demonstrate a 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 (q-time scale).

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BibTeX RIS

Wenqing Hu. 2016-09-19. It\^o's formula, the stochastic exponential and change of measure on general time scales. https://arxiv.org/abs/1609.05967

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