Limit theorems of probability theory and optimality in linear controlled systems with quadratic cost

2006 ◽  
pp. 316-329 ◽  
Author(s):  
Petr Mandl
Keyword(s):  
Probability Theory ◽  
Limit Theorems ◽  
Controlled Systems ◽  
Quadratic Cost ◽  
Linear Controlled Systems

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.

Limit Theorems of Probability Theory

2011 ◽  
pp. 742-744
Author(s):  
Alexandr Alekseevich Borovkov
Keyword(s):  
Probability Theory ◽  
Limit Theorems

Limit Theorems in Probability Theory

1969 ◽  
pp. 150-202
Author(s):  
Yu. V. Prohorov ◽  
Yu. A. Rozanov
Keyword(s):  
Probability Theory ◽  
Limit Theorems

scholarly journals Some recent advances for limit theorems

2020 ◽  
Vol 68 ◽  
pp. 73-96 ◽  
Author(s):  
Benjamin Arras ◽  
Jean-Christophe Breton ◽  
Aurelia Deshayes ◽  
Olivier Durieu ◽  
Raphaël Lachièze-Rey
Keyword(s):  
Probability Theory ◽  
Stochastic Geometry ◽  
Limit Theorems ◽  
Growth Models ◽  
Rates Of Convergence ◽  
Discrete Models ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Correlated Random Walks ◽  
Recent Developments

We present some recent developments for limit theorems in probability theory, illustrating the variety of this field of activity. The recent results we discuss range from Stein’s method, as well as for infinitely divisible distributions as applications of this method in stochastic geometry, to asymptotics for some discrete models. They deal with rates of convergence, functional convergences for correlated random walks and shape theorems for growth models.

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