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Fractional Brownian motion [PDF]
, 2006 There are natural phenomena in which wide variability is commonly observed, most notably the weather. Any expectations of regularity, or independence of this year’s weather from the past or the future, are not borne out by tradition or folklore. Mandelbrot and Wallis [16.1] saw the essence of traditional knowledge expressed in the Old Testament ...
Oksana Banna +3 more
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Fractional Brownian Motions [PDF]
Acta Physica Polonica B, 2020 Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ.
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Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion [PDF]
Theory of Probability & Its Applications, 2022 Рассматривается вероятность персистентности для интегрированного дробного броуновского движения и дробно интегрированного броуновского движения с параметром $H$. Для интегрированного дробного броуновского движения обсуждается гипотеза Молчана- Хохлова и устанавливается асимптотическое поведение показателя персистентности при $H\to0$ и при $H\to1 ...
Aurzada, F., Kilian, M.
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Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion
Complexity, 2021 This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed ...
Weijun Ma +3 more
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Oscillatory Fractional Brownian Motion [PDF]
Acta Applicandae Mathematicae, 2013 The authors ``introduce oscillatory analogues of fractional Brownian motion [(fBm)], subfractional Brownian motion [(sfBm)] and other related long range dependent Gaussian processes.'' According to them, the oscillatory fractional Brownian motion (ofBm) is a centered Gaussian process \(\xi ^{H}\), with parameter \(H\in (1/2,1)\) and covariance function
Bojdecki, T. +2 more
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ON THE QHASI CLASS AND ITS EXTENSION TO SOME GAUSSIAN SHEETS
International Journal for Computational Civil and Structural Engineering, 2022 Introduced in 2018 the generalized bifractional Brownian motion is considered as an element of the quasi-helix with approximately stationary increment class of real centered Gaussian processes conditioning by parameters.
Charles El-Nouty, Darya Filatova
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Trading Fractional Brownian Motion
SIAM Journal on Financial Mathematics, 2017 The authors consider a market with an asset price described by fractional Brownian motion, which can be traded with temporary nonlinear price impact. The asymptotically optimal strategies for the maximization of expected terminal wealth are obtained.
Paolo Guasoni +2 more
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Journal of Mathematics, 2022 In this paper, we consider the fractional-stochastic Boussinesq-Burger system (FSBBS) generated by the multiplicative Brownian motion. The Jacobi elliptic function techniques are used to create creative elliptic, hyperbolic, and rational fractional ...
Wael W. Mohammed +2 more
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Frontiers in Physics, 2021 In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion.
Lili Gao, Xichao Sun
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On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes
Mathematics, 2019 We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss−Markov process from Doob representation by replacing ...
Mario Abundo, Enrica Pirozzi
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