Results 91 to 100 of about 243,967 (218)
Abstract and Applied Analysis, 2014 Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that
Kaili Xiang, Yindong Zhang, Xiaotong Mao
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Mathematics, 2020 We introduce three new estimators of the drift parameter of a fractional Ornstein–Uhlenbeck process. These estimators are based on modifications of the least-squares procedure utilizing the explicit formula for the process and covariance structure of a ...
Pavel Kříž, Leszek Szała
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An Itô-type formula for the fractional Brownian motion in Brownian time
Electronic Journal of Probability, 2014 19 ...
Nourdin, Ivan, Zeineddine, Raghid
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ON SPECTRAL SIMULATION OF FRACTIONAL BROWNIAN MOTION [PDF]
Probability in the Engineering and Informational Sciences, 2003 This article focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this article, we study the class of approximate methods that are based on the
Michel Mandjes, A. B. Dieker
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The Multiparameter Fractional Brownian Motion [PDF]
arXiv, 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 L\'evy fractional Brownian motion and with the fractional Brownian sheet are discussed.
arxiv
Stochastic delay fractional evolution equations driven by fractional Brownian motion [PDF]
, 2014 In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An application to the stochastic fractional heat equation is presented to illustrate the theory.
arxiv +1 more source
The renormalization group and fractional Brownian motion [PDF]
Physics Letters A, 2002 We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the Renormalization Group as a tool to improve perturbative calculations, and check that beyond the classical regime of ...
Juan Pérez-Mercader, David Hochberg
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Asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time [PDF]
arXiv, 2016 We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time Z_t:= X_{Y_t}, t >= 0, where X is a fractional Brownian motion and Y is an independent Brownian motion.
arxiv
Transfer Principle for nth Order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law [PDF]
arXiv, 2018 The $n$th order fractional Brownian motion was introduced by Perrin et al. It is the (upto a multiplicative constant) unique self-similar Gaussian process with Hurst index $H \in (n-1,n)$, having $n$th order stationary increments. We provide a transfer principle for the $n$th order fractional Brownian motion, i.e., we construct a Brownian motion from ...
arxiv
Tempered Fractional Brownian Motion Revisited Via Fractional Ornstein-Uhlenbeck Processes [PDF]
arXiv, 2019 Tempered fractional Brownian motion is revisited from the viewpoint of reduced fractional Ornstein-Uhlenbeck process. Many of the basic properties of the tempered fractional Brownian motion can be shown to be direct consequences or modifications of the properties of fractional Ornstein-Uhlenbeck process.
arxiv