scholarly journals Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails

2020 ◽  
Vol 23 (3) ◽  
pp. 553-570
Author(s):  
Alexander Gushchin ◽  
Ilya Pavlyukevich ◽  
Marian Ritsch
Keyword(s):  
Heavy Tails ◽  
Uhlenbeck Process ◽  
Drift Estimation ◽  
Ornstein Uhlenbeck Process

CONTROLLED DRIFT ESTIMATION IN FRACTIONAL DIFFUSION LINEAR SYSTEMS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250025 ◽  
Author(s):  
ALEXANDRE BROUSTE ◽  
CHUNHAO CAI
Keyword(s):  
Maximum Likelihood ◽  
Laplace Transform ◽  
Fractional Diffusion ◽  
Likelihood Estimator ◽  
Uhlenbeck Process ◽  
Drift Estimation ◽  
Partially Observed ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

This paper is devoted to the determination of the asymptotical optimal input for the estimation of the drift parameter in a partially observed but controlled fractional Ornstein–Uhlenbeck process. Large sample asymptotical properties of the Maximum Likelihood Estimator are deduced using Ibragimov–Khasminskii program and Laplace transform computations.

scholarly journals A CORRELATED STOCHASTIC VOLATILITY MODEL MEASURING LEVERAGE AND OTHER STYLIZED FACTS

2002 ◽  
Vol 05 (05) ◽  
pp. 541-562 ◽  
Author(s):  
JAUME MASOLIVER ◽  
JOSEP PERELLÓ
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Leverage Effect ◽  
Stylized Facts ◽  
Uhlenbeck Process ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Negative Skewness

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

scholarly journals Using the Ornstein–Uhlenbeck process to model the evolution of interacting populations

2017 ◽  
Vol 429 ◽  
pp. 35-45 ◽  
Author(s):  
Krzysztof Bartoszek ◽  
Sylvain Glémin ◽  
Ingemar Kaj ◽  
Martin Lascoux
Keyword(s):  
Uhlenbeck Process ◽  
Interacting Populations ◽  
Ornstein Uhlenbeck Process
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