Results 11 to 20 of about 37,159 (330)
Generalized fractional Brownian motion [PDF]
Modern Stochastics: Theory and Applications, 2017 We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena.
Mounir Zili
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The Multiparameter Fractional Brownian Motion [PDF]
, 2006 We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the
Herbin, Erick, Merzbach, Ely
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Mixed Fractional Brownian Motion [PDF]
Bernoulli, 2001 Let \(B\) be the standard Brownian motion and \(B^H\) fractional Brownian motion with Hurst index \(H\in (0,1]\). If the Brownian motion \(B\) and the fractional Brownian motion \(B^H\) are independent and \(\alpha\in\mathbb{R} \setminus \{0\}\), define the mixed fractional Brownian motion \(M^{H,\alpha}\) by \(M^{H,\alpha} \doteq B+\alpha B^H\).
Patrick Cheridito
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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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Stochastic volatility and fractional Brownian motion
Stochastic Processes and their Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnaud Gloter, Marc Hoffmann
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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, Frank, Kilian, Martin
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Approximations of fractional Brownian motion [PDF]
Bernoulli, 2011 Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process.
Li, Yuqiang, Dai, Hongshuai
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Local independence of fractional Brownian motion
Stochastic Processes and their Applications, 2007 Let S(t,t') be the sigma-algebra generated by the differences X(s)-X(s) with s,s' in the interval(t,t'), where (X_t) is the fractional Brownian motion process with Hurst index H between 0 and 1. We prove that for any two distinct t and t' the sigma-algebras S(t-a,t+a) and S(t'-a,t'+a) are asymptotically independent as a tends to 0.
Ilkka Norros, Eero Saksman
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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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On Squared Fractional Brownian Motions [PDF]
, 2004 We have proved recently that fractional Brownian motions with Hurst parameter H in (0, 1/2) satisfy a remarkable property: their squares are infinitely divisible. In the Brownian motion case (the case H = 1/2), this property is completely understood thanks to stochastic calculus arguments.
Eisenbaum, N., Tudor, C.A.
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