Limit theorems for Jacobi ensembles with large parameters

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.

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Central Limit Theorems for Weighted Sums of Dependent Random Vectors in Hilbert Spaces via the Theory of the Regular Variation

Journal of Theoretical Probability ◽

10.1007/s10959-021-01079-4 ◽

2021 ◽

Author(s):

Ta Cong Son ◽

Le Van Dung

Keyword(s):

Central Limit ◽

Hilbert Spaces ◽

Regular Variation ◽

Limit Theorems ◽

Central Limit Theorems ◽

Weighted Sums ◽

Random Vectors

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

Journal of Applied Probability ◽

10.1017/jpr.2020.82 ◽

2021 ◽

Vol 58 (1) ◽

pp. 197-216 ◽

Cited By ~ 1

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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Law of large numbers and central limit theorems through Jack generating functions

Advances in Mathematics ◽

10.1016/j.aim.2020.107545 ◽

2021 ◽

Vol 380 ◽

pp. 107545

Author(s):

Jiaoyang Huang

Keyword(s):

Central Limit ◽

Generating Functions ◽

Limit Theorems ◽

Law Of Large Numbers ◽

Central Limit Theorems ◽

Large Numbers

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

Advances in Applied Probability ◽

10.1017/apr.2020.35 ◽

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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Pressure Function and Limit Theorems for Almost Anosov Flows

Communications in Mathematical Physics ◽

10.1007/s00220-021-03962-x ◽

2021 ◽

Vol 382 (1) ◽

pp. 1-47

Author(s):

Henk Bruin ◽

Dalia Terhesiu ◽

Mike Todd

Keyword(s):

Thermodynamic Properties ◽

Central Limit ◽

Limit Theorems ◽

Central Limit Theorems ◽

Stable Laws ◽

Analytic Framework ◽

Pressure Function ◽

Hyperbolic Flows ◽

Anosov Flows ◽

Almost Anosov

AbstractWe obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

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