Quantile sensitivity estimation for dependent sequences

2016 ◽  
Vol 53 (3) ◽  
pp. 715-732
Author(s):  
Guangxin Jiang ◽  
Michael C. Fu
Keyword(s):  
Limit Theorem ◽  
Weak Consistency ◽  
Infinitesimal Perturbation Analysis ◽  
Regenerative Processes ◽  
Uhlenbeck Process ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Sensitivity Estimation ◽  
Ornstein Uhlenbeck Process ◽  
Infinitesimal Perturbation

AbstractIn this paper we estimate quantile sensitivities for dependent sequences via infinitesimal perturbation analysis, and prove asymptotic unbiasedness, weak consistency, and a central limit theorem for the estimators under some mild conditions. Two common cases, the regenerative setting and ϕ-mixing, are analyzed further, and a new batched estimator is constructed based on regenerative cycles for regenerative processes. Two numerical examples, the G/G/1 queue and the Ornstein–Uhlenbeck process, are given to show the effectiveness of the estimator.

scholarly journals Stochastic Theories and Deterministic Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-29
Author(s):  
John F. Moxnes ◽  
Kjell Hausken
Keyword(s):  
Quantum Theory ◽  
Differential Equations ◽  
Wigner Function ◽  
Quantum Physics ◽  
Stochastic Theory ◽  
Uhlenbeck Process ◽  
Numerical Examples ◽  
Quantum Equation ◽  
Ornstein Uhlenbeck Process

We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared.

Fluctuations near homogeneous states of chemical reactions with diffusion

1987 ◽  
Vol 19 (2) ◽  
pp. 352-370 ◽  
Author(s):  
Peter Kotelenez
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Limit Theorem ◽  
Chemical Reactions ◽  
Stochastic Partial Differential Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Homogeneous State ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

Conditions are given under which a space-time jump Markov process describing the stochastic model of non-linear chemical reactions with diffusion converges to the homogeneous state solution of the corresponding reaction-diffusion equation. The deviation is measured by a central limit theorem. This limit is a distribution-valued Ornstein–Uhlenbeck process and can be represented as the mild solution of a certain stochastic partial differential equation.

A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes

2016 ◽  
Vol 53 (1) ◽  
pp. 22-32 ◽  
Author(s):  
Qing-Pei Zang ◽  
Li-Xin Zhang
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Unknown Parameter ◽  
Extended Model ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Ornstein Uhlenbeck Process ◽  
Interest Rate Model

AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

Fluctuations near homogeneous states of chemical reactions with diffusion

1987 ◽  
Vol 19 (02) ◽  
pp. 352-370
Author(s):  
Peter Kotelenez
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Limit Theorem ◽  
Chemical Reactions ◽  
Stochastic Partial Differential Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Homogeneous State ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

Conditions are given under which a space-time jump Markov process describing the stochastic model of non-linear chemical reactions with diffusion converges to the homogeneous state solution of the corresponding reaction-diffusion equation. The deviation is measured by a central limit theorem. This limit is a distribution-valued Ornstein–Uhlenbeck process and can be represented as the mild solution of a certain stochastic partial differential equation.

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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