fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the...

Stratonovich Brownian rough path. More generally, let B H ( t ) {\displaystyle B_{H}(t)} be a multidimensional fractional Brownian motion (a process whose...

many ways of defining the elevation function. For instance, the fractional Brownian motion variable may be used, or various rotation functions may be used...

stationary increments asymptotically, the most typical one being fractional Brownian motion. In the converse, given a self-similar process with stationary...

{\displaystyle \alpha } for FGN is equal to H {\displaystyle H} . For fractional Brownian motion (FBM), we have β ∈ [ 1 , 3 ] {\displaystyle \beta \in [1,3]} ...

questioned. It has been found that log-volatility behaves as a fractional Brownian motion with Hurst exponent of order H = 0.1 {\displaystyle H=0.1} , at...

independent of all of the values before this. According to a model of Fractional Brownian motion this is referred to as long memory of positive linear autocorrelation...

E.g., both Markov processes (i.e., memory-free processes) and fractional Brownian motion scale at the level of 1-point densities (simple averages), but...

visual effects. The modeling of the Earth's rough surfaces via fractional Brownian motion was first proposed by Benoit Mandelbrot. Because the intended...

calculus, and probability theory. Topics in her research include fractional Brownian motion and portfolio optimization for inside traders. She is a professor...

the following Generalizations of Brownian motion, such as the fractional Brownian motion and scaled Brownian motion Diffusion in fractals and percolation...

electronic devices. In their study of fractional Brownian motion, Mandelbrot and Van Ness proposed the name fractional noise (sometimes since called fractal...

quasiperiodic torii). The dynamics has been described as deterministic fractional Brownian motion, and exhibits anomalous diffusion. Thomas, René (1999). "Deterministic...

The Brownian bridge is (like the Ornstein–Uhlenbeck process) an example of a Gaussian process whose increments are not independent. The fractional Brownian...

integration against both semimartingales and processes such as the fractional Brownian motion. The Choquet integral, a subadditive or superadditive integral...

Recent research has demonstrated that anomalous diffusion in fractional Brownian motion (fBm) models can effectively characterize typical animal movement...

introduction to white–noise theory and Malliavin calculus for fractional Brownian motion". Proceedings of the Royal Society of London A: Mathematical,...

Cellular automata Computational creativity Fractal landscape Fractional Brownian motion Generative art Generative artificial intelligence L-systems Linear...

kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach". Annals of Operations Research. 299 (1–2). springer...

self-similarity and fractional dimension, B. Mandelbrot Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin (2001). "The Dimension of the Planar Brownian Frontier...

literature are semimartingales, this is not always the case. Fractional Brownian motion with Hurst parameter H ≠ 1/2 is not a semimartingale. The semimartingales...

valid for the systems with ergodicity, like classical Brownian motion (BM), fractional Brownian motion (fBM), and continuous-time random walk (CTRW) with...

Compound Poisson process Wiener process Geometric Brownian motion Fractional Brownian motion Brownian bridge Ornstein–Uhlenbeck process Gamma process Markov...

example, this approach leads to an easy prediction formula for the Fractional Brownian motion. In a non-intrusive setting, the estimation of the expansion coefficients...

similar. Fractional calculus — fractional differentiation Differintegral — fractional integration and differentiation Fractional Brownian motion — a continuous-time...

(or Brownian motion) is self-similar with H = 1 / 2 {\displaystyle H=1/2} . The fractional Brownian motion is a generalisation of Brownian motion that...

Ballistic Missile, of the United States Navy Fogg Behavior Model Fractional Brownian motion (fBm) Frankfurt Book Fair (Frankfurter Buchmesse), a book trade...

D_{F}\{\cdot \}} is the Hausdorff dimension of a point set. Fractal Fractional Brownian motion Hausdorff dimension van den Berg, J. C. (2004), Wavelets in Physics...

{G}}_{T}(f)} . We can calculate the Hausdorff dimension of the fractional Brownian motion B H {\displaystyle B^{H}} of Hurst index 1 / α = H ∈ ( 0 , 1 ]...

Fokker–Planck equation, which is usually used to model Brownian motion. The equation requires the use of fractional derivatives. For jump lengths which have a symmetric...