Computing statistics for fractional Brownian motion
Large deviations of Shepp statistics for fractional Brownian motion
... Numerous authors have considered properties and characterisations of fBm, see e.g., Mishura and Valkeila (2011), Kabluchko (2011b) and the references therein. Our contribution present a new result for the Shepp ...
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CiteSeerX — The fractional Brownian motion
... H-fBm is H-self-similar and has stationary increments. For H = 1 2 , fractional Brownian motion is standard Brownian motion and denoted by W . FBm is interesting from a theoretical ...
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Arbitrage with fractional brownian motion?
... Since fractional Brownian motion is not a semimartingale (except in the Brownian motion case), stock price processes (fully or partially) driven by a fractional Brownian ...
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Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?
... a Brownian motion is typically used in modeling the asset prices, interest rates and ex- change rates, and so ...of Brownian motion as a driving force of the underlying asset price processes ...
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CiteSeerX — Representations of Fractional Brownian Motion
... 1.2. Statement of problem and result We have seen some well known examples of representations of fractional Brownian motion. Notice that the Molchan-Golosov representation requires integration only ...
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An extension of sub-fractional Brownian motion
... The self similarity and stationarity of the increments are two main prop- erties for which fBm enjoyed success as modeling tool in telecommuni- cations and finance. The sfBm is an extension of Bm which preserves many ...
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Fractional Brownian motion: theory and applications
... This paper aims to give a few aspects of the recent theory and applications of the fractional Brownian motion. We begin by the construction of the process for which recent theoretical advances ...
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Fractional Brownian Motion with a Reflecting Wall
... 2018) Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous ...analyze fractional Brownian ...
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Fractional Brownian motion and weather derivatives
... integral, fractional Itô formula and fractional Girsanov theorem, as well as to make a sketch of a arbitrage-free model for temperature based ...analysis, fractional white noise, Fourier transform, ...
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Transformation formulas for fractional Brownian motion
... name fractional Brownian motion was proposed by Mandelbrot and Van Ness in 1968, when they described fBm by a Wiener integral process of a fractional integral kernel, ...
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Prediction law of fractional Brownian motion
... Brownian motion with parameter H > 1 2 based on observations extending to the infinite ...the fractional Brownian motion is well understood, it seems that the regular conditional law ...
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Estimation of the drift of fractional Brownian motion
... [4] James, W., Stein, C., 1961. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. 1,361- 379. [5] Kolmogorov, A. N., 1940. Wienersche Spiralen ...
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Cylindrical fractional Brownian motion in Banach spaces
... to fractional integral and derivative ...the fractional Ornstein-Uhlenbeck process as the mild and weak solution of a abstract stochastic Cauchy problem in a Banach ...with fractional noise in a ...
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The quadratic variation for mixed fractional Brownian motion
... standard Brownian motion independent of B H and λ, ν ∈ R \ { } ...that Brownian motion B in the mixed-fBm W can offset some irregularity of fBm such that the theoretical issues for them ...
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Weak convergence of the complex fractional Brownian motion
... Statistics and econometrics have made great progress in the last two decades. It became necessary to study the distributions or the asymptotic distributions of some complex statistics, so the weak ...
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Stochastic integration with respect to the fractional Brownian motion
... The purpose of our paper is to develop a stochastic calculus with respect to the fractional Brownian motion B with Hurst parameter H > 2 1 using the techniques of the Malliavin calculus. Unlike ...
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The valuation of currency options by fractional Brownian motion
... the fractional Black–Scholes market presents no arbitrage opportunity and is ...the fractional Brownian ...obtain fractional Black–Scholes formulas for pricing options, including Necula (2002) ...
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The Application of Fractional Brownian Motion in Option Pricing
... the Brownian Motion changes in asset prices , and sports scores relatively Brown with incremental inter -related nature, Using it to study some of the characteristics of asset prices which better reflect ...
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STOCHASTIC INTEGRATION WITH RESPECT TO FRACTIONAL BROWNIAN MOTION
... make fractional Brownian motion a natural can- didate as a model of noise in mathematical finance (see Comte and Re- nault [5], Rogers [26]), and in communication networks (see, for instance, Leland, ...
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Evaluation of the Fractional Brownian Motion Model of Terrain
... U nfortunately, the row /colum n algorithm had already been applied to th e Alpine, Ger m an and USA datasets. The D eadm ann B u tte and M ontagne Sainte Victoire DEMs provide case instances for the regional and ...
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