scholarly journals Limit theorems for discrete-time metapopulation models

2010 ◽  
Vol 7 (0) ◽  
pp. 53-83 ◽  
Author(s):  
F.M. Buckley ◽  
P.K. Pollett
Keyword(s):  
Discrete Time ◽  
Limit Theorems ◽  
Metapopulation Models

scholarly journals Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

2021 ◽  
Vol 58 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Jörn Sass ◽  
Dorothee Westphal ◽  
Ralf Wunderlich
Keyword(s):  
Stock Returns ◽  
Financial Market ◽  
Discrete Time ◽  
High Frequency ◽  
Utility Maximization ◽  
Limit Theorems ◽  
Approximate Solutions ◽  
Diffusion Approximations ◽  
Expert Opinions ◽  
Arrival Intensity

AbstractThis paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

Interplay between Local Dynamics and Dispersal in Discrete-time Metapopulation Models

2002 ◽  
Vol 218 (3) ◽  
pp. 273-288 ◽  
Author(s):  
ABDUL-AZIZ YAKUBU ◽  
CARLOS CASTILLO-CHAVEZ
Keyword(s):  
Discrete Time ◽  
Local Dynamics ◽  
Metapopulation Models

scholarly journals Realization of the probability laws in the quantum central limit theorems by a quantum walk

2013 ◽  
Vol 13 (5&6) ◽  
pp. 430-438
Author(s):  
Takuya Machida
Keyword(s):  
Probability Theory ◽  
Limit Theorem ◽  
Central Limit ◽  
Discrete Time ◽  
Limit Theorems ◽  
Quantum Walk ◽  
Quantum Probability ◽  
Quantum Walks ◽  
Central Limit Theorems ◽  
Initial State

Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there are four notions of independence (free, monotone, commuting, and boolean independence) and quantum central limit theorems associated to each independence have been investigated. The relation between quantum walks and quantum probability theory is still unknown. As random walks are fundamental models in the Kolmogorov probability theory, can the quantum walks play an important role in quantum probability theory? To discuss this problem, we focus on a discrete-time 2-state quantum walk with a non-localized initial state and present a limit theorem. By using our limit theorem, we generate probability laws in the quantum central limit theorems from the quantum walk.

Discrete-Time Approximations and Limit Theorems

2021 ◽  
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko
Keyword(s):  
Discrete Time ◽  
Limit Theorems

scholarly journals Limit Theorems for Discrete-Time Quantum Walks on Trees

2009 ◽  
Vol 15 (3) ◽  
pp. 423-429 ◽  
Author(s):  
Kota CHISAKI ◽  
Masatoshi HAMADA ◽  
Norio KONNO ◽  
Etsuo SEGAWA
Keyword(s):  
Discrete Time ◽  
Limit Theorems ◽  
Quantum Walks ◽  
Time Quantum

MARTINGALE APPROXIMATION OF NON-STATIONARY STOCHASTIC PROCESSES

2006 ◽  
Vol 06 (02) ◽  
pp. 173-183 ◽  
Author(s):  
DALIBOR VOLNÝ
Keyword(s):  
Large Deviations ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Invariance Principle ◽  
Limit Theorems ◽  
Orlicz Spaces ◽  
Stationary Case ◽  
Martingale Approximation ◽  
Stationary Stochastic Processes ◽  
Log Law

We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log–log law, probabilities of large deviations) are studied.

A continuous time Markov branching model with random environments

1973 ◽  
Vol 5 (1) ◽  
pp. 37-54 ◽  
Author(s):  
Norman Kaplan
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Population Model ◽  
Limit Theorems ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Random Environments ◽  
Markov Branching Process ◽  
Branching Model ◽  
Necessary And Sufficient

A population model is constructed which combines the ideas of a discrete time branching process with random environments and a continuous time non-homogeneous Markov branching process. The extinction problem is considered and necessary and sufficient conditions for extinction are determined. Also discussed are limit theorems for what corresponds to the supercritical case.

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