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Economics letters, ISSN 0165-1765, 08/2016, Volume 145, pp. 52 - 55

Fractional Brownian motion embeds Brownian motion as a special case and offers more flexible diffusion component for pricing models...

Hurst index test | Finite jumps | Bi-power variation | Fractional Brownian motion | G12 | C12 | Economics | Business & Economics | Social Sciences | Studies | Simulation | Indexes | Brownian movements

Hurst index test | Finite jumps | Bi-power variation | Fractional Brownian motion | G12 | C12 | Economics | Business & Economics | Social Sciences | Studies | Simulation | Indexes | Brownian movements

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 1/2006, Volume 36, Issue 4, pp. 1249 - 1284

Multifractional Brownian motion is an extension of the well-known fractional Brownian motion...

Brownian motion | Determinism | Covariance | White noise | Mathematical independent variables | Fourier transformations | Mathematical functions | Trajectories | Mathematics | Contrapuntal motion | Hölder regularity | Local asymptotic self-similarity | Fractional Brownian motion | Multi-parameter processes | Gaussian processes | Physical Sciences | Science & Technology | Probability | 60 G 17 | 60 G 18 | local asymptotic self-similarity | multi-parameter processes | 60 G 15

Brownian motion | Determinism | Covariance | White noise | Mathematical independent variables | Fourier transformations | Mathematical functions | Trajectories | Mathematics | Contrapuntal motion | Hölder regularity | Local asymptotic self-similarity | Fractional Brownian motion | Multi-parameter processes | Gaussian processes | Physical Sciences | Science & Technology | Probability | 60 G 17 | 60 G 18 | local asymptotic self-similarity | multi-parameter processes | 60 G 15

Journal Article

Applied and computational harmonic analysis, ISSN 1063-5203, 11/2019

Journal Article

New journal of physics, ISSN 1367-2630, 02/2019, Volume 21, Issue 2, p. 022002

Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes...

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Economic models | Stochastic processes | Boundary conditions | Organelles | Probability density functions | Convergence | Particle density (concentration) | Depletion | Gaussian process | Tracer diffusion | Random walk theory | Diffusion | Brownian movements | Microfluidics | Deposition

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Economic models | Stochastic processes | Boundary conditions | Organelles | Probability density functions | Convergence | Particle density (concentration) | Depletion | Gaussian process | Tracer diffusion | Random walk theory | Diffusion | Brownian movements | Microfluidics | Deposition

Journal Article

Physica A, ISSN 0378-4371, 10/2011, Volume 390, Issue 20, pp. 3592 - 3601

... properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst indexes H∈(0,1...

Fractality | Horizontal visibility graph | Dynamics | Fractional Brownian motion | Mixing pattern | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Networks | Horizontal | Fractal analysis | Graphs | Fractals | Visibility | Topology | Coefficients

Fractality | Horizontal visibility graph | Dynamics | Fractional Brownian motion | Mixing pattern | Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Networks | Horizontal | Fractal analysis | Graphs | Fractals | Visibility | Topology | Coefficients

Journal Article

Metrika, ISSN 0026-1335, 3/2009, Volume 69, Issue 2, pp. 125 - 152

We study the local times of fractional Brownian motions for all temporal dimensions, N, spatial dimensions d and Hurst parameters H for which local times exist. We establish...

Statistics for Business/Economics/Mathematical Finance/Insurance | Local times | Law of the iterated logarithm | Economic Theory | Probability Theory and Stochastic Processes | Statistics, general | Statistics | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Statistics for Business/Economics/Mathematical Finance/Insurance | Local times | Law of the iterated logarithm | Economic Theory | Probability Theory and Stochastic Processes | Statistics, general | Statistics | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology

Journal Article

The Annals of probability, ISSN 0091-1798, 11/2009, Volume 37, Issue 6, pp. 2200 - 2230

We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H = 1/4...

Brownian motion | Cauchy Schwarz inequality | Mathematical theorems | Particle collisions | Integration by parts | Mathematics | Random variables | Hermite polynomials | Particle trajectories | Laws of Motion | Weak convergence | Change of variable formula | Malliavin calculus | Quartic process | Weighted quadratic variations | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Science & Technology | Mathematics - Probability | Probability | weighted quadratic variations | change of variable formula | quartic process | 60H07 | weak convergence | 60H05 | 60F05 | 60G15

Brownian motion | Cauchy Schwarz inequality | Mathematical theorems | Particle collisions | Integration by parts | Mathematics | Random variables | Hermite polynomials | Particle trajectories | Laws of Motion | Weak convergence | Change of variable formula | Malliavin calculus | Quartic process | Weighted quadratic variations | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Science & Technology | Mathematics - Probability | Probability | weighted quadratic variations | change of variable formula | quartic process | 60H07 | weak convergence | 60H05 | 60F05 | 60G15

Journal Article

Journal of theoretical probability, ISSN 0894-9840, 9/2018, Volume 31, Issue 3, pp. 1539 - 1589

We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time $$Z_t:= X_{Y_t},t \geqslant 0$$
Zt:=XYt...

60G22 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Limit theorem | Fractional Brownian motion in Brownian time | Weighted power variations | 60H07 | Malliavin calculus | 60H05 | Fractional Brownian motion | 60F05 | 60G15 | Statistics & Probability | Physical Sciences | Science & Technology | Wavelet transforms | Asymptotic properties | Brownian movements

60G22 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Limit theorem | Fractional Brownian motion in Brownian time | Weighted power variations | 60H07 | Malliavin calculus | 60H05 | Fractional Brownian motion | 60F05 | 60G15 | Statistics & Probability | Physical Sciences | Science & Technology | Wavelet transforms | Asymptotic properties | Brownian movements

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 12/2018, Volume 51, Issue 49, p. 495001

.... This paper pays attention to a special stochastic process, tempered fractional Langevin motion, which is non-Markovian and undergoes ballistic diffusion for long times...

inverse β-stable subordinator | time-changed Langevin system | time-changed tempered fractional Brownian motion | Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Physics - Statistical Mechanics

inverse β-stable subordinator | time-changed Langevin system | time-changed tempered fractional Brownian motion | Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Physics - Statistical Mechanics

Journal Article

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 08/2019, Volume 25, Issue 3, pp. 2137 - 2162

We study the issue of integration with respect to the non-commutative fractional Brownian motion, that is the analog of the standard fractional Brownian motion in a non-commutative probability setting...

Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Probability | Operator Algebras

Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Probability | Operator Algebras

Journal Article

Advances in applied probability, ISSN 0001-8678, 12/2015, Volume 47, Issue 4, pp. 1108 - 1131

Fractional Lévy processes generalize fractional Brownian motion in a natural way...

General Applied Probability | Fractional Ornstein-Uhlenbeck process | Shot-noise process | Generalized fractional Lévy process | Fractional Lévy process | Functional central limit theorem | Stochastic volatility model | Regular variation | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical functions | Stochastic models | Volatility | Brownian movements | Approximations | Kernels | Brownian motion | Approximation | Ornstein-Uhlenbeck process | Mathematical analysis | Stochastic processes | Stochasticity | 60G22 | 62P20 | 60G51 | 91B28 | fractional Brownian motion | stochastic volatility model | functional central limit theorem | fractional Lévy process | 91B24 | fractional Ornstein-Uhlenbeck process | generalized fractional Lévy process | 60F17 | regular variation

General Applied Probability | Fractional Ornstein-Uhlenbeck process | Shot-noise process | Generalized fractional Lévy process | Fractional Lévy process | Functional central limit theorem | Stochastic volatility model | Regular variation | Fractional Brownian motion | Statistics & Probability | Physical Sciences | Mathematics | Science & Technology | Studies | Mathematical functions | Stochastic models | Volatility | Brownian movements | Approximations | Kernels | Brownian motion | Approximation | Ornstein-Uhlenbeck process | Mathematical analysis | Stochastic processes | Stochasticity | 60G22 | 62P20 | 60G51 | 91B28 | fractional Brownian motion | stochastic volatility model | functional central limit theorem | fractional Lévy process | 91B24 | fractional Ornstein-Uhlenbeck process | generalized fractional Lévy process | 60F17 | regular variation

Journal Article

Journal of theoretical probability, ISSN 0894-9840, 6/2019, Volume 32, Issue 2, pp. 721 - 736

In this paper, we present Chung’s functional law of the iterated logarithm for increments of a fractional Brownian motion...

60G22 | Chung’s functional law of the iterated logarithm | Increments | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Fractional Brownian motion | 60F17 | 60F15 | Statistics & Probability | Physical Sciences | Science & Technology | Brownian movements | Theorems | Random walk theory

60G22 | Chung’s functional law of the iterated logarithm | Increments | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Fractional Brownian motion | 60F17 | 60F15 | Statistics & Probability | Physical Sciences | Science & Technology | Brownian movements | Theorems | Random walk theory

Journal Article

Journal of theoretical probability, ISSN 1572-9230, 06/2018, Volume 32, Issue 3, pp. 1581 - 1612

We consider the drawdown and drawup of a fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in a financial market...

Drawup | Primary 60G15 | Secondary 60G70 | Probability Theory and Stochastic Processes | Geometric fractional Brownian motion | Piterbarg constant | Mathematics | Statistics, general | Fractional Brownian motion | Pickands constant | Drawdown | Statistics & Probability | Physical Sciences | Science & Technology | Financial markets | Asymptotic properties | Brownian movements | Random walk theory

Drawup | Primary 60G15 | Secondary 60G70 | Probability Theory and Stochastic Processes | Geometric fractional Brownian motion | Piterbarg constant | Mathematics | Statistics, general | Fractional Brownian motion | Pickands constant | Drawdown | Statistics & Probability | Physical Sciences | Science & Technology | Financial markets | Asymptotic properties | Brownian movements | Random walk theory

Journal Article

Chaos, solitons and fractals, ISSN 0960-0779, 11/2018, Volume 116, pp. 54 - 62

•We constructed a very promising and interesting statistical testing procedure for identification of the fractional Brownian motion in empirical data...

Fractional brownian motion | Detrending moving average algorithm | Statistical test | Mathematics, Interdisciplinary Applications | Physical Sciences | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Physics | Science & Technology

Fractional brownian motion | Detrending moving average algorithm | Statistical test | Mathematics, Interdisciplinary Applications | Physical Sciences | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Physics | Science & Technology

Journal Article

Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems, ISSN 1572-9311, 01/2019, Volume 22, Issue 3, pp. 323 - 357

In this paper, we consider the problem of estimating the lead–lag parameter between two stochastic processes driven by fractional Brownian motions (fBMs...

60G22 | Non-synchronous observations | Contrast estimation | Lead–lag effect | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | 62M09 | Fractional Brownian motion | Stochastic processes | Analysis | Numerical analysis | Economic models | Parameter estimation | Computer simulation | Process parameters | Mathematical models | Ion migration | Stochastic models | Convergence

60G22 | Non-synchronous observations | Contrast estimation | Lead–lag effect | Probability Theory and Stochastic Processes | Statistical Theory and Methods | Mathematics | 62M09 | Fractional Brownian motion | Stochastic processes | Analysis | Numerical analysis | Economic models | Parameter estimation | Computer simulation | Process parameters | Mathematical models | Ion migration | Stochastic models | Convergence

Journal Article

IEEE transactions on information theory, ISSN 0018-9448, 03/2014, Volume 60, Issue 3, pp. 1963 - 1975

We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion...

scaling | high frequency financial data | Biological system modeling | Noise | Stochastic processes | multifractal random walk | Fractals | Calculus | Brownian motion | leverage effect | Mathematical model | Malliavin calculus | Fractional Brownian motion | infinitely divisible cascades | Computer Science, Information Systems | Engineering, Electrical & Electronic | Engineering | Technology | Computer Science | Science & Technology | Signal processing | Usage | Numerical analysis | Integral equations | Innovations | Mathematical models | Simulation | Brownian movements

scaling | high frequency financial data | Biological system modeling | Noise | Stochastic processes | multifractal random walk | Fractals | Calculus | Brownian motion | leverage effect | Mathematical model | Malliavin calculus | Fractional Brownian motion | infinitely divisible cascades | Computer Science, Information Systems | Engineering, Electrical & Electronic | Engineering | Technology | Computer Science | Science & Technology | Signal processing | Usage | Numerical analysis | Integral equations | Innovations | Mathematical models | Simulation | Brownian movements

Journal Article