Some limit theorems for summability methods of I.I.D.Random variables

1987 ◽  
pp. 57-68 ◽  
Author(s):  
Makoto Maejima
Keyword(s):  
Limit Theorems ◽  
Summability Methods

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

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.

scholarly journals Limit theorems for multi-type general branching processes with population dependence

2020 ◽  
Vol 52 (4) ◽  
pp. 1127-1163
Author(s):  
Jie Yen Fan ◽  
Kais Hamza ◽  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Population Model ◽  
General Framework ◽  
Limit Theorems ◽  
Mating Systems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Special Section ◽  
Large Numbers ◽  
Type Population

AbstractA general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

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