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New Journal of Physics, ISSN 1367-2630, 2015, Volume 17, Issue 6, p. 63038
We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal... 
Ageing | Stochastic processes | Anomalous diffusion | ageing | GRANULAR GASES | FRACTIONAL DYNAMICS | SELF-DIFFUSION | NONERGODICITY | INTRACELLULAR-TRANSPORT | PHYSICS, MULTIDISCIPLINARY | PLASMA-MEMBRANE | SINGLE-MOLECULE DIFFUSION | KINETIC-THEORY | RANDOM-WALKS | anomalous diffusion | stochastic processes
Journal Article
1990, ISBN 9780821824849, Volume no. 420., iv, 128
Book
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 2, p. 123558
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. The main result is an asymptotic... 
Spectral problem | Fractional Brownian motion | Small ball probabilities | Gaussian processes
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 06/2019, Volume 123, pp. 347 - 355
Forecasting non-stationary stochastic time series represents a rather complex problem. The reason is that such temporal series are not only self-similar but... 
Fractional Brown motion | Maximum likelihood algorithm | Stochastic partial differential equation | Long-range dependence | Difference equation | SELF-SIMILARITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | HURST EXPONENT | PHYSICS, MATHEMATICAL | PARAMETER
Journal Article
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. We propose test statistics... 
Hurst index test | Finite jumps | Bi-power variation | Fractional Brownian motion | G12 | C12 | BIPOWER VARIATION | RETURNS | ECONOMICS | JUMPS
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2019, p. 122955
Journal Article
Bernoulli, ISSN 1350-7265, 05/2018, Volume 24, Issue 2, pp. 895 - 925
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2019, Volume 526, p. 121002
We construct a time-fractional geometric Fokker–Planck equation from the diffusion limit of a continuous time random walk with a power law waiting time... 
Geometric Brownian motion | Continuous time random walks | Anomalous diffusion | Subdiffusion | Fractional Fokker–Planck equation | Fractional Fokker-Planck equation | PHYSICS, MULTIDISCIPLINARY | FINANCE | MASTER-EQUATIONS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2018, Volume 51, Issue 43, p. 435001
We analyse the power spectral density (PSD) S-T(f) (with T being the observation time and f the frequency) of a fractional Brownian motion (fBm), with an... 
power spectral density | stochastic reset | fractional Brownian motion | POWER SPECTRUM | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics | Condensed Matter | Physics | Statistical Mechanics
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 03/2018, Volume 134, pp. 70 - 78
We study an extension of the ARCH model that includes the squared fractional Brownian motion. We study the statistical properties of the model as the... 
ARCH model | Stationary process | Volatility | Fractional Brownian motion | STATISTICS & PROBABILITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2019, Volume 472, Issue 1, pp. 11 - 21
We extend the Burkholder–Davis–Gundy inequalities for fractional Brownian motions with the Hurst index less than 1/2, completing the proof of... 
Fractional Brownian motion | The Burkholder–Davis–Gundy inequalities | MATHEMATICS | MATHEMATICS, APPLIED | FORMULA | The Burkholder-Davis-Gundy inequalities
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2020, Volume 100, p. 106006
In this paper, an averaging principle for multidimensional, time dependent, stochastic differential equations (SDEs) driven by fractional Brownian motion and... 
Pathwise Riemann–Stieltjes integral | Averaging principle | Fractional Brownian motion | Itô stochastic calculus
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 10/2017, Volume 129, pp. 155 - 166
We calculate the regular conditional future law of the fractional Brownian motion with index conditioned on its past. We show that the conditional law is... 
Regular conditional law | Fractional Brownian motion | Prediction | STATISTICS & PROBABILITY | GAUSSIAN-PROCESSES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2018, Volume 458, Issue 2, pp. 1678 - 1692
Let be a real valued fractional Brownian motion with Hurst index and let be an inverse -stable subordinator independent of . The inverse stable subordinator... 
Inverse of α-stable subordinator | Tail probability | Fractional Brownian motion | Large deviation | MATHEMATICS | MATHEMATICS, APPLIED | TIME RANDOM-WALKS | THEOREMS | Inverse of alpha-stable subordinator
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2018, Volume 51, Issue 49, p. 495001
Time-changed stochastic processes have attracted much attention and wide interest due to their extensive applications, especially in financial time series,... 
inverse β-stable subordinator | time-changed Langevin system | time-changed tempered fractional Brownian motion | TIME RANDOM-WALKS | PHYSICS, MULTIDISCIPLINARY | inverse beta-stable subordinator | EQUATIONS | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2018, Volume 494, pp. 8 - 16
In this paper, we explore the pricing of the assets of Asian rainbow options under the condition that the assets have self-similar and long-range dependence... 
Rainbow options | Asian options | Fractional Brownian motion | Monte Carlo simulation | LONG-RANGE DEPENDENCE | PHYSICS, MULTIDISCIPLINARY
Journal Article
Bernoulli, ISSN 1350-7265, 11/2017, Volume 23, Issue 4B, pp. 3571 - 3597
We prove the following result: For (Z(t))t is an element of R a fractional Brownian motion with arbitrary Hurst parameter, for any stopping timer, there exist... 
Two-way crossing | Stopping time | Fractional Brownian motion | Law of the iterated logarithm | stopping time | law of the iterated logarithm | TRANSACTION COSTS | STATISTICS & PROBABILITY | ARBITRAGE | fractional Brownian motion | two-way crossing
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 02/2020, Volume 157, p. 108628
Bifractional Brownian motion on is a two parameter centered Gaussian process with covariance function: This process has been originally introduced by Houdré... 
Self-similar processes | Fractional Brownian motion | Positive definite functions | Bifractional Brownian motion | Gaussian processes
Journal Article
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