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1. Full Text Tempering stable processes
by Rosiński, Jan
Stochastic Processes and their Applications, ISSN 0304-4149, 2007, Volume 117, Issue 6, pp. 677 - 707
A tempered stable Lévy process combines both the -stable and Gaussian trends. In a short time frame it is close to an -stable process while in a long time... 
Tempered stable distributions and processes | Stable processes | Shot noise representations | Lévy processes | Ornstein–Uhlenbeck-type processes | Ornstein-Uhlenbeck-type processes | shot noise representations | STOCHASTIC-PROCESS | REPRESENTATIONS | stable processes | Levy processes | CONVERGENCE | STATISTICS & PROBABILITY | tempered stable distributions and processes | Tempered stable distributions and processes Stable processes Lévy processes Ornstein-Uhlenbeck-type processes Shot noise representations
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2. Full Text A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process
by Wang, Weiming and Cai, Yongli and Ding, Zuqin and Gui, Zhanji
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 509, pp. 921 - 936
In this paper, based on the results of Gray et al. (2011), we propose a new SDE SIS model incorporating mean-reverting Ornstein–Uhlenbeck process, and prove... 
Persistence | Intensity of volatility | Speed of reversion | Ornstein–Uhlenbeck process | Stochastic basic reproduction number | Extinction | Ornstein-Uhlenbeck process | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | STATIONARY DISTRIBUTION | ENVIRONMENTAL VARIABILITY | DYNAMICS | Epidemics | Models | Disease transmission | Analysis | Differential equations
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3. Full Text Integrated stationary Ornstein–Uhlenbeck process, and double integral processes
by Abundo, Mario and Pirozzi, Enrica
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 03/2018, Volume 494, pp. 265 - 275
We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process in terms of Brownian motion ; moreover, we show that, under... 
Gauss–Markov process | Double integral process | Ornstein–Uhlenbeck process | BROWNIAN-MOTION | Ornstein-Uhlenbeck process | PHYSICS, MULTIDISCIPLINARY | 1ST HITTING TIME | ADAPTATION | SPIKE TRAIN | MODEL | Gauss-Markov process
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4. Full Text Ergodic aspects of some Ornstein–Uhlenbeck type processes related to Lévy processes
by Bertoin, Jean
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2019, Volume 129, Issue 4, pp. 1443 - 1454
This work concerns the Ornstein–Uhlenbeck type process associated to a positive self-similar Markov process which drifts to , namely . We point out that is... 
Stationarity | Ornstein–Uhlenbeck type process | Self-similar Markov process | Darling–Kac theorem | Lévy process | Exponential functional | SIMILAR MARKOV-PROCESSES | Darling-Kac theorem | Levy process | CONVERGENCE | STATISTICS & PROBABILITY | DRIVEN | Ornstein-Uhlenbeck type process | EXPONENTIAL FUNCTIONALS | Markov processes
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5. Full Text Law equivalence of Ornstein–Uhlenbeck processes driven by a Lévy process
by Bartosz, Grzegorz and Kania, Tomasz
Indagationes Mathematicae, ISSN 0019-3577, 09/2019, Volume 30, Issue 5, pp. 796 - 804
We demonstrate that two Ornstein–Uhlenbeck processes, that is, solutions to certain stochastic differential equations that are driven by a Lévy process have... 
Lévy–itô decomposition | Wiener process | Ornstein–Uhlenbeck process | SDE | Girsanov’s theorem | Lévy process | SPACE | MATHEMATICS | Ornstein-Uhlenbeck process | Levy process | Levy-ito decomposition | Girsanov's theorem | Laws, regulations and rules | Differential equations
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6. Full Text Ornstein–Uhlenbeck process with fluctuating damping
by Eab, Chai Hok and Lim, S.C
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2018, Volume 492, pp. 790 - 803
This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the... 
Dichotomous noise | Multiplicative noise | Ornstein–Uhlenbeck process | Fractional Gaussian noise | Langevin equation | BROWNIAN-MOTION | MOMENT INSTABILITIES | Ornstein-Uhlenbeck process | HARMONIC-OSCILLATOR | PHYSICS, MULTIDISCIPLINARY | PARAMETERS | STOCHASTIC-FREQUENCY | KINETICS | GROWTH | SYSTEMS | DIFFUSION
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7. Full Text Strong approximation rate for Wiener process by fast oscillating integrated Ornstein–Uhlenbeck processes
by Li, Junlin and Fu, Hongbo and He, Ziying and Zhang, Yiwei
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 08/2018, Volume 113, pp. 314 - 325
In this paper, we use fast oscillating integrated Ornstein–Uhlenbeck (abbreviated as O-U) processes to pathwisely approximate Wiener processes. In physics,... 
Integrated Ornstein–Uhlenbeck processes | Pathwise approximation for stochastic differential equations | Stochastic evolution equations | Approximation of random invariant manifolds | STOCHASTIC DIFFERENTIAL-EQUATIONS | TIMES | PHYSICS, MULTIDISCIPLINARY | NOISE | DRIVEN | PHYSICS, MATHEMATICAL | WONG-ZAKAI APPROXIMATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Integrated Ornstein-Uhlenbeck processes | CONVERGENCE | MANIFOLDS
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8. Full Text Ornstein–Uhlenbeck process, Cauchy process, and Ornstein–Uhlenbeck–Cauchy process on a circle
by Liu, Cheng-Shi
Applied Mathematics Letters, ISSN 0893-9659, 09/2013, Volume 26, Issue 9, pp. 957 - 962
By a simple mathematical method, we obtain the transition probability density functions of the Ornstein–Uhlenbeck process, Cauchy process, and... 
Ornstein–Uhlenbeck–Cauchy process | Transition probability density | Cauchy process | Ornstein–Uhlenbeck process | Ornstein-Uhlenbeck process | Ornstein-Uhlenbeck-Cauchy process | MATHEMATICS, APPLIED
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9. Full Text Time-changed Ornstein-Uhlenbeck process
by Gajda, Janusz and Wyłomańska, Agnieszka
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2015, Volume 48, Issue 13, pp. 135004 - 18
The Ornstein-Uhlenbeck process is one of the most popular systems used for financial data description. However, this process has also been examined in the... 
Subordination | Covariance | Fractional Fokker-Planck equation | Ornstein-Uhlenbeck process | Functions (mathematics) | Simulation | Mathematical analysis | Finance | Mathematical models | Inverse | Biology
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10. Full Text Sparse inference of the drift of a high-dimensional Ornstein–Uhlenbeck process
by Gaïffas, Stéphane and Matulewicz, Gustaw
Journal of Multivariate Analysis, ISSN 0047-259X, 01/2019, Volume 169, pp. 1 - 20
Given the observation of a high-dimensional Ornstein–Uhlenbeck (OU) process in continuous time, we are interested in inference on the drift parameter under a... 
High-dimensional statistics | Ornstein–Uhlenbeck process | Sparse estimation | Lasso | STATISTICS & PROBABILITY | Ornstein-Uhlenbeck process | SELECTION
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11. Full Text Pricing weather derivatives with partial differential equations of the Ornstein–Uhlenbeck process
by Li, Peng
Computers and Mathematics with Applications, ISSN 0898-1221, 02/2018, Volume 75, Issue 3, pp. 1044 - 1059
This paper means to price weather derivatives through solving the Partial Differential Equation (PDE) of the Ornstein–Uhlenbeck process. Since the PDE is... 
PDE | Ornstein–Uhlenbeck process | Convection–diffusion | Jump condition | Weather derivative | MATHEMATICS, APPLIED | Ornstein-Uhlenbeck process | Convection-diffusion | DIFFUSION | Monte Carlo method | Aquatic resources | Pricing | Differential equations
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12. Some metric order of entropy-properties of an infinite-dimensional Ornstein-Uhlenbeck process
by Koski, Timo
1985, ISBN 9789516491373, 22
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13. Full Text Extremes of q-Ornstein–Uhlenbeck processes
by Wang, Yizao
Stochastic Processes and their Applications, ISSN 0304-4149, 09/2018, Volume 128, Issue 9, pp. 2979 - 3005
Two limit theorems are established on the extremes of a family of stationary Markov processes, known as -Ornstein–Uhlenbeck processes with . Both results are... 
Markov process | Self-similar process | Excursion probability | Tangent process | Semi-min-stable process | [formula omitted]-Ornstein–Uhlenbeck process | Double-sum method | Brown–Resnick process | q-Ornstein–Uhlenbeck process | SAMPLE | GAUSSIAN RANDOM-FIELDS | Brown-Resnick process | q-Ornstein-Uhlenbeck process | STATISTICS & PROBABILITY | ERGODIC PROPERTIES | Markov processes
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14. Full Text SCOUP: Probabilistic model based on the Ornstein-Uhlenbeck process to analyze single-cell expression data during differentiation
by Matsumoto, Hirotaka and Kiryu, Hisanori
BMC Bioinformatics, ISSN 1471-2105, 06/2016, Volume 17, Issue 1, p. 232
Background: Single-cell technologies make it possible to quantify the comprehensive states of individual cells, and have the power to shed light on cellular... 
Single-cell transcriptomics | Differentiation analysis | Ornstein-Uhlenbeck process | HETEROGENEITY | BIOTECHNOLOGY & APPLIED MICROBIOLOGY | CHEMOKINES | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | EMBRYOS | FATE DECISIONS | Cell Line | Reproducibility of Results | Area Under Curve | Humans | Gene Expression Regulation | Models, Statistical | Gene Regulatory Networks | Transcription Factors - metabolism | Cell Differentiation - genetics | Cell Lineage | Algorithms | Stochastic Processes | Time Factors | Single-Cell Analysis - methods | Principal Component Analysis | Gene Ontology | Cluster Analysis | Gene expression | Observations
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15. Full Text Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations
by Bartoszek, Krzysztof and Glémin, Sylvain and Kaj, Ingemar and Lascoux, Martin and Linköpings universitet and Institutionen för datavetenskap and Statistik och maskininlärning and Filosofiska fakulteten
Journal of Theoretical Biology, ISSN 0022-5193, 09/2017, Volume 429, pp. 35 - 45
The Ornstein–Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process... 
Phylogenetic comparative methods | Ornstein–Uhlenbeck process | Species interactions | Trait evolution | Migration | STATES | QUANTITATIVE TRAITS | Ornstein-Uhlenbeck process | WITHIN-SPECIES VARIATION | TREES | ADAPTATION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STABILIZING SELECTION | PHYLOGENETIC COMPARATIVE-ANALYSIS | ADAPTIVE EVOLUTION | Adaptation, Physiological | Biological Evolution | Animal Migration - physiology | Biological Variation, Population - physiology | Phenotype | Phylogeny | Evolution | Evolutionary biology | Analysis | Models | Plant genetics | Biological Sciences | Migration; Ornstein-Uhlenbeck process; Phylogenetic comparative methods; Species interactions; Trait evolution | Naturvetenskap | Biologiska vetenskaper | Evolutionsbiologi | Natural Sciences | Evolutionary Biology
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16. Full Text Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes
by El Machkouri, Mohamed and Es-Sebaiy, Khalifa and Ouknine, Youssef
Journal of the Korean Statistical Society, ISSN 1226-3192, 09/2016, Volume 45, Issue 3, pp. 329 - 341
The statistical analysis for equations driven by fractional Gaussian process (fGp) is relatively recent. The development of stochastic calculus with respect to... 
Parameter estimation | Non-ergodic Gaussian Ornstein–Uhlenbeck process | Non-ergodic Gaussian Ornstein-Uhlenbeck process | STATISTICS & PROBABILITY | Brownian motion | Models | Analysis | Gaussian processes | Least squares | Probability | Mathematics | 통계학
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17. Full Text Time-changed Ornstein-Uhlenbeck process
by Gajda, J and Wylomanska, A
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 04/2015, Volume 48, Issue 13
The Ornstein-Uhlenbeck process is one of the most popular systems used for financial data description. However, this process has also been examined in the... 
Ornstein-Uhlenbeck process | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL BROWNIAN-MOTION | PEARSON DIFFUSIONS | covariance | MODEL | PHYSICS, MATHEMATICAL | fractional Fokker-Planck equation | ANOMALOUS DIFFUSION | RANDOM-WALKS | DYNAMICS | PLANCK-KOLMOGOROV EQUATIONS | FINANCIAL DATA | subordination
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18. Full Text Detecting Anomalous Deviations From Standard Maritime Routes Using the Ornstein-Uhlenbeck Process
by d'Afflisio, Enrica and Braca, Paolo and Millefiori, Leonardo M and Willett, Peter
IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2018, Volume 66, Issue 24, pp. 6474 - 6487
A novel anomaly detection procedure based on the Ornstein-Uhlenbeck (OU) mean-reverting stochastic process is presented. The considered anomaly is a vessel... 
Spaceborne radar | long term prediction of vessel motion | Maritime surveillance | real-world data | Transponders | Anomaly detection | radar | maritime anomaly detection | statistical hypothesis test | target tracking | automatic identification system | Trajectory | Ornstein–Uhlenbeck process | Artificial intelligence | Marine vehicles | Ornstein-Uhlenbeck process | maritime surveillance | ALGORITHMS | RADARS | PREDICTION | ENGINEERING, ELECTRICAL & ELECTRONIC | PROBABILITY | SURVEILLANCE | FRAMEWORK | Hypotheses | Stochastic processes | Switches | False alarms | Process parameters
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19. Full Text Pattern and Process in the Comparative Study of Convergent Evolution
by Mahler, D. Luke and Weber, Marjorie G and Wagner, Catherine E and Ingram, Travis
AMERICAN NATURALIST, ISSN 0003-0147, 08/2017, Volume 190, Issue S1, pp. S13 - S28
Understanding processes that have shaped broad-scale biodiversity patterns is a fundamental goal in evolutionary biology. The development of phylogenetic... 
INTERSPECIFIC COMPETITION | ADAPTIVE RADIATIONS | convergence | ORNSTEIN-UHLENBECK MODELS | MORPHOLOGICAL CONVERGENCE | phylogenetic comparative methods | adaptation | CHARACTER STATES | POPULATION-GENETICS | EVOLUTIONARY BIOLOGY | ECOLOGICAL OPPORTUNITY | adaptive radiation | ECOLOGY | STABILIZING SELECTION | evolutionary process | PHYLOGENETIC COMPARATIVE-ANALYSIS | TRAIT EVOLUTION | Biological Evolution | Phylogeny | Biodiversity | Fossils
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20. Full Text Exact pathwise simulation of multi-dimensional Ornstein–Uhlenbeck processes
by de la Cruz, H and Jimenez, J. C
Applied Mathematics and Computation, ISSN 0096-3003, 02/2020, Volume 366, p. 124734
The exact pathwise simulation of multidimensional Ornstein–Uhlenbeck processes is considered. We propose two procedures that allow the exact pathwise... 
Pathwise simulation | Stochastic differential equations | Ornstein–Uhlenbeck process | Exact simulation | MATHEMATICS, APPLIED | Ornstein-Uhlenbeck process | DRIVEN | MODEL
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