Itô's formula, the stochastic exponential and change of measure on general time scales

2016/09/19 by Wenqing Hu, Hu, Wenqing
Economics, Econometrics and Finance · Mathematics · #34N05 #60H10 #60J60 #60J65 #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1609.05967

openalex publication_date 2016/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an Itô's 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 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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