In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process BH(t) on [0, T], that starts at zero, has expectation zero for all t in [0, T], and has the following covariance function: 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. It was introduced by . The value of H determines what kind of process the fBm is: * if H = 1/2 then the process is in fact a Brownian motion or Wiener process; * if H > 1/2 then the increments of the process are positively correlated; * if H < 1/2 then the increments of the process are negatively correlated. The increment process, X(t) = BH(t+1) − BH(t), is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: n-th order fractional Brownian motion, abbreviated as n-fBm. n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order n are stationary. For n = 1, n-fBm is classical fBm. Like the Brownian motion that it generalizes, fractional Brownian motion is named after 19th century biologist Robert Brown; fractional Gaussian noise is named after mathematician Carl Friedrich Gauss. (Wikipedia).
AWESOME Brownian motion (with explanation)!
Brownian motion is the random motion of particles suspended in a fluid resulting from their collision with the fast-moving molecules in the fluid. This pattern of motion typically alternates random fluctuations in a particle's position inside a fluid subdomain with a relocation to anoth
From playlist THERMODYNAMICS
Accelerated motion and oscillation!
In this video i demonstrate accelerated motion with interface. I show the graphs of simple accelerating motion and simple harmonic motion with force and motion sensor!
From playlist MECHANICS
Circular Motion - A Level Physics
Consideration of Circular Motion, orbital speed, angular speed, centripetal acceleration and force - with some worked example.
From playlist Classical Mechanics
Fractional Brownian motion with Hurst index H=0 and the Gaussian unitary ensemble - Khoruzhenko
Boris Khoruzhenko Queen Mary and Westfield College November 8, 2013 For more videos, please visit http://video.ias.edu
From playlist Mathematics
In this second part on Motion, we take a look at calculating the velocity and position vectors when given the acceleration vector and initial values for velocity and position. It involves as you might imagine some integration. Just remember that when calculating the indefinite integral o
From playlist Life Science Math: Vectors
C67 The physics of simple harmonic motion
See how the graphs of simple harmonic motion changes with changes in mass, the spring constant and the values correlating to the initial conditions (amplitude)
From playlist Differential Equations
Asymptotic properties of the volatility estimator from high-frequency data modeled by Ananya Lahiri
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Takashi Kumagai: Time changes of stochastic processes: convergence and heat kernel estimates
Abstract: In recent years, interest in time changes of stochastic processes according to irregular measures has arisen from various sources. Fundamental examples of such time-changed processes include the so-called Fontes-Isopi-Newman (FIN) diffusion and fractional kinetics (FK) processes,
From playlist Probability and Statistics
Mohamed Ndaoud - Constructing the fractional Brownian motion
In this talk, we give a new series expansion to simulate B a fractional Brownian motion based on harmonic analysis of the auto-covariance function. The construction proposed here reveals a link between Karhunen-Loève theorem and harmonic analysis for Gaussian processes with stationarity co
From playlist Les probabilités de demain 2017
Sandro Franceschi : Méthode des invariants de Tutte et mouvement brownien réfléchi dans des cônes
Résumé : Dans les années 1970, William Tutte développa une approche algébrique, basée sur des "invariants", pour résoudre une équation fonctionnelle qui apparait dans le dénombrement de triangulations colorées. La transformée de Laplace de la distribution stationnaire du mouvement brownien
From playlist Probability and Statistics
From playlist Contributed talks One World Symposium 2020
Dynamical phase transitions in Markov processes by Hugo Touchette
COLLOQUIUM DYNAMICAL PHASE TRANSITIONS IN MARKOV PROCESSES SPEAKER: Hugo Touchette (Stellenbosch University, South Africa) DATE: Mon, 15 July 2019, 15:00 to 16:00 VENUE:Emmy Noether Seminar Room, ICTS Campus, Bangalore ABSTRACT Dynamical phase transitions (DPTs) are phase transitio
From playlist ICTS Colloquia
Large deviations for the Wiener Sausage by Frank den Hollander
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Some solvable Stochastic Control Problems
At the 2013 SIAM Annual Meeting, Tyrone Duncan of the University of Kansas described stochastic control problems for continuous time systems where optimal controls and optimal costs can be explicitly determined by a direct method. The applicability of this method is demonstrated by example
From playlist Complete lectures and talks: slides and audio
Dynamical properties of a tagged particle in single file by Tridip Sadhu
PROGRAM URL : http://www.icts.res.in/program/NESP2015 DATES : Monday 26 Oct, 2015 - Friday 20 Nov, 2015 VENUE : Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : This program will be organized as an advanced discussion workshop on some topical issues in nonequilibrium statstical phys
From playlist Non-equilibrium statistical physics
Physics 3: Motion in 2-D (16 of 21) Circular Motion and Acceleration
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain circular motion, acceleration, and centripetal acceleration.
From playlist PHYSICS - MECHANICS
Probabilistic methods in statistical physics for extreme statistics... - 19 September 2018
http://crm.sns.it/event/420/ Probabilistic methods in statistical physics for extreme statistics and rare events Partially supported by UFI (Université Franco-Italienne) In this first introductory workshop, we will present recent advances in analysis, probability of rare events, search p
From playlist Centro di Ricerca Matematica Ennio De Giorgi