# fractional Brownian motion

### FRACTIONAL BROWNIAN MOTION AND STANDARD BROWNIAN MOTION

... Shevchenko, Existence and uniqueness of the solution of stochastic differential equation involving wiener process and fractional Brownian motion with Hurst index H > 1/2, Comm.. R˘ a¸[r] ...

14

### 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 ...

14

### Arbitrage with fractional brownian motion?

... a fractional Brown- ian motion starting at −∞ , and subsequently by Cheridito [8], taking only the history starting from 0 into ...the fractional Brownian ...

12

### 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 ...

11

### 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 ...

84

### CiteSeerX — REMARKS ON THE FRACTIONAL BROWNIAN MOTION

... There are many ways to tackle the fractional Brownian motion. In this paper, we use a convolution of a white noise by a distribution T . This distribution operates in principal value as explained in ...

14

### An extension of sub-fractional Brownian motion

... Abstract: In this paper, firstly, we introduce and study a self-similar Gaussian process with parameters H ∈ (0, 1) and K ∈ (0,1] that is an extension of the well known sub-fractional Brownian motion ...

12

### 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 ...

12

### 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 ...

6

### 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, ...

17

### Prediction law of fractional Brownian motion

... LAURI VIITASAARI Department of Mathematics and System Analysis, Aalto University School of Science, Helsinki, P.O. Box 11100, FIN-00076 Aalto, FINLAND Abstract. We calculate the regular conditional future law of the ...

14

### Estimation of the drift of fractional Brownian motion

... d-dimensional fractional Brownian motion (fBm) defined on the probability space (Ω, F, P ...dimensional fractional Brownian motions with Hurst parameter H ∈ (0, 1), ...

13

### Cylindrical fractional Brownian motion in Banach spaces

... CYLINDRICAL FRACTIONAL BROWNIAN MOTION IN BANACH SPACES ELENA ISSOGLIO AND MARKUS RIEDLE ...cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic ...

31

### The quadratic variation for mixed fractional Brownian motion

... Regularizing Fractional Brownian Motion with a Miew towards Stock Price ...The fractional mixed fractional Brownian ...a fractional mixed fractional Brownian ...

20

### Weak convergence of the complex fractional Brownian motion

... complex fractional Brownian motion from a standard Poisson process and from a Lévy process, respectively, by the method in Delgado and Jolis ...

18

### 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 ...

25

### The valuation of currency options by fractional Brownian motion

... Abstract This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differ- ential ...

15

### The Application of Fractional Brownian Motion in Option Pricing

... Movement; Fractional Brownian Motion; Options; Volatility ...Brown Motion theory is usually used for researching the change of asset price in previous option pricing theory, while ...

10

### 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, ...

40

### Basic properties of the Multivariate Fractional Brownian Motion

... the fractional Brownian motion has been a question of great interest in the ...a fractional Gaussian ...the fractional Gaussian noise, it can be proved that the circulant matrix is ...

22