Stochastic Convergence and Limit Theorems

2019 ◽  
pp. 136-168
Author(s):  
Narayan C. Giri
Keyword(s):  
Limit Theorems ◽  
Stochastic Convergence

QUANTUM DECOMPOSITION IN DISCRETE GROUPS AND INTERACTING FOCK SPACES

2001 ◽  
Vol 04 (02) ◽  
pp. 277-287 ◽  
Author(s):  
YUKIHIRO HASHIMOTO
Keyword(s):  
Limit Theorems ◽  
Discrete Group ◽  
Free Groups ◽  
Length Function ◽  
Discrete Groups ◽  
Fock Spaces ◽  
Stochastic Convergence ◽  
Poisson Transform ◽  
Stochastic Limit ◽  
General Stochastic

We introduce a kind of quantum decomposition of generators of a discrete group with a suitable length function and construct a sequence of one-mode interacting Fock spaces associated with a filtration of the group. We show stochastic convergence of such a sequence of interacting Fock spaces and obtain a general stochastic limit theorems on discrete groups. As an application to free groups, we see that the Haagerup states give rise to a Gaussian–Poisson transform through its coherent expression.

Limit theorems and price changes in financial markets

1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Limit Theorems ◽  
Price Changes

Limit theorems for long-memory flows on Wiener chaos

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1473-1503 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Memory ◽  
Limit Theorems ◽  
Wiener Chaos

ON GENERALIZED STOCHASTIC CONVERGENCE

1994 ◽  
Vol 20 (2) ◽  
pp. 450
Author(s):  
Larson
Keyword(s):  
Stochastic Convergence

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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.

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