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LOCAL TIME OF MIXED BROWNIAN MOTION AND SUBFRACTIONAL BROWNIAN MOTION

Jingjun Guo, Yafang Zhang

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Abstract

In this article, local time of mixed Brownian motion and subfractional Brownian motion is studied. By using an alternative expression of subfractional Brownian motion, it is proved that the local time is a Hida distribution through white noise approach. Moreover, the chaos expansion of the local time is given by S-transform. Lastly, regularized condition of the local time is also obtained. Some results of local time of Brownian motion are popularized.

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What this paper is about

In this article, local time of mixed Brownian motion and subfractional Brownian motion is studied. By using an alternative expression of subfractional Brownian motion, it is proved that the local time is a Hida distribution through white noise approach. Moreover, the chaos expansion of the local time is given by S-transform. Lastly, regularized condition of the local time is also obtained. Some results of local time of Brownian motion are popularized.

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Available abstract

In this article, local time of mixed Brownian motion and subfractional Brownian motion is studied. By using an alternative expression of subfractional Brownian motion, it is proved that the local time is a Hida distribution through white noise approach. Moreover, the chaos expansion of the local time is given by S-transform. Lastly, regularized condition of the local time is also obtained. Some results of local time of Brownian motion are popularized.

Key concepts: Brownian motion, Local time, Fractional Brownian motion, Diffusion process, Mathematics, Brownian excursion, Reflected Brownian motion, Geometric Brownian motion

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