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Non-Analytic Solution to the Fokker-Planck Equation of Fractional Brownian Motion via Laplace Transforms

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  • Visant Ahuja

Abstract

This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper obtains the transition probability density function of the random variable that is described by the It\^o's stochastic ordinary differential equation of fractional Brownian motion. Furthermore, this paper applies the derived transition probability density function to the Cox-Ingersoll-Ross model governed by the fractional Brownian motion instead of the usual Brownian motion.

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  • Visant Ahuja, 2017. "Non-Analytic Solution to the Fokker-Planck Equation of Fractional Brownian Motion via Laplace Transforms," Papers 1704.00256, arXiv.org.
    • Handle: RePEc:arx:papers:1704.00256
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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