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# Approximation of fractional brownian motion by martingales

##### 2019-11-15 02:43

Another form of fractional Brownian motion is Liouville fractional Brownian motion (LfBm), , where the kernel K 1 (t, s) is replaced by K 2 (t, s) (t s) H 1 2, that is a stochastic process defined bymotion by martingales, precisely, we are interested how far is fractional Brownian motion from being a martingale. That is, in a sense, we look for the projection of fractional Brownian motion on approximation of fractional brownian motion by martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense.

## Approximation of fractional brownian motion by martingales free

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation

Abstract: We find an approximation in the space of a fractional Brownian motion by martingales of the form, where is a Wiener process, is a power function with a negative index, that is where, , and is the index of fractional Brownian motion.

where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness of the resultant motion, with a higher value leading to a smoother motion.

Approximation of Fractional Brownian Motion by Martingales Approximation of Fractional Brownian Motion by Martingales Shklyar, Sergiy; Shevchenko, Georgiy; Mishura, Yuliya; Doroshenko, Vadym; Banna, Oksana 00: 00: 00 We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation

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Abstract: We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form.

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