# Fractional Brownian Motion

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## Fractional Brownian Motion

A biased random walk. Unlike Standard Brownian Motion, the odds are biased in one direction or the other. It is like playing with loaded dice.

## Fractional Brownian Motion

A random walk with some bias. That is, fractional Brownian motion means that a security's price moves seemingly randomly, but with some external event sending it in one direction or the other.
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References in periodicals archive ?
The increment of the fractional Brownian motion [DELTA][B.
Fractional order stochastic differential equation driven by a fractional Brownian motion (FSDE) is defined as follows:
H](t) is fractional Brownian motion, [mu](X, t) is the drift parameter of stochastic process, and [sigma](X, t) is the diffusion coefficient.
Assume that the price of the spot and the futures follows a stochastic differential equation driven by the fractional Brownian motion, the price equation of the stock is
S] is the memory parameter of the spot price, [mathematical expression not reproducible] is the fractional Brownian motion, is the drift coefficient of the stock process, and as is the diffusion coefficient of the stock process.
Cheridito, "Arbitrage in fractional Brownian motion models," Finance and Stochastics, vol.
Zhang, "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and Its Applications, vol.
Feng, "Study of lookback option pricing in fractional Brownian motion environment," The Journals of North China University of Technology, vol.
Lin, "Stochastic analysis of fractional Brownian motion," Stochastic and Stochastic Reports, vol.
Stochastic calculus for fractional Brownian motion 1.
Option pricing in a fractional Brownian motion environment.
Pricing currency options in a fractional Brownian motion with jumps.

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