Results 11 to 20 of about 24,420 (193)
Ornstein-Uhlenbeck-Cauchy Process [PDF]
Journal of Mathematical Physics, 1999 We combine earlier investigations of linear systems with L\'{e}vy fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)].
Cambanis +19 more
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On Ornstein–Uhlenbeck driven by Ornstein–Uhlenbeck processes [PDF]
Statistics & Probability Letters, 2014 We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.
Bernard Bercu +2 more
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Spherical Ornstein-Uhlenbeck Processes [PDF]
Journal of Statistical Physics, 2011 The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterized by only one dimensionless number, the persistence angle, which is the typical angle of rotation of the object during the correlation time of the angular ...
Wilkinson, Michael, Pumir, Alain
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The elliptical Ornstein–Uhlenbeck process
Statistics and Its Interface, 2023 We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are observed in many applications of coupled bivariate time series.
Sykulski, AM +2 more
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Generalized Ornstein-Uhlenbeck processes [PDF]
Journal of Mathematical Physics, 2006 We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [Ornstein and Uhlenbeck, Phys. Rev. 36, 823 (1930)]. Our generalized Ornstein-Uhlenbeck systems include a force which depends upon the position of the particle, as well as upon time.
Bezuglyy, V. +4 more
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Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes
Axioms, 2022 In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a ...
Maria C. Mariani +3 more
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Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting
Mathematics, 2023 The Ornstein–Uhlenbeck (O-U) process with resetting is considered as the anomalous transport taking place on a three-dimensional comb. The three-dimensional comb is a comb inside a comb structure, consisting of backbones and fingers in the following ...
Pece Trajanovski +3 more
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Spurious ergodicity breaking in normal and fractional Ornstein–Uhlenbeck process
New Journal of Physics, 2020 The Ornstein–Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to ...
Yousof Mardoukhi +2 more
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Markov-modulated Ornstein–Uhlenbeck processes [PDF]
Advances in Applied Probability, 2016 Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and
Huang, G. +5 more
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Modern Stochastics: Theory and Applications, 2014 European call option issued on a bond governed by a modified geometric Ornstein-Uhlenbeck process, is investigated. Objective price of such option as a function of the mean and the variance of a geometric Ornstein-Uhlenbeck process is studied.
Yu. Mishura, G. Rizhniak, V. Zubchenko
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