The ?empirical law of large numbers? or ?The stability of frequencies?

1972 ◽  
Vol 4 (4) ◽  
pp. 484-490 ◽  
Author(s):  
H. Freudenthal
Keyword(s):  
Law Of Large Numbers ◽  
Large Numbers ◽  
Empirical Law ◽  
The Stability

Destiny, Being and the Empirical Law of Large Numbers

2020 ◽  
Vol 6 (1) ◽  
pp. 77
Author(s):  
Rosario D’Amico
Keyword(s):  
Law Of Large Numbers ◽  
Large Numbers ◽  
Empirical Law ◽  
Reading Key

The aim of this paper is to give a practical meaning to the term ”possible”, which can then become a useful reading key to attempt to decipher the nature and functioning of the so-called Being, that is, of being-in-itself, of the reality implied, of what there is behind what it is. Thanks to this hermeneutic tool together with the singular existential experience of Mister Tanat`o, the imaginary protagonist of this treatment, we will interpret the Being as all that is pre-destined - that is, as the set of fundamental conditions for (there to be) such being [essente] or nothingness - and sensitive reality as all that is destined - that is, as the rotation of the guided evolutions of the Being -. Finally, to confirm and investigate the results we have achieved, we will provide a solution both to the hypothetical paradox of prediction, in which the apparent antinomy lies in admitting that predictions can be subsequently falsified, and to an interesting probabilistic problem.

On stability of nonlinear AR processes with Markov switching

2000 ◽  
Vol 32 (2) ◽  
pp. 394-407 ◽  
Author(s):  
J.-F. Yao ◽  
J.-G. Attali
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Stability Problem ◽  
Law Of Large Numbers ◽  
Markov Switching ◽  
Strong Law ◽  
Large Numbers ◽  
Nonlinear Autoregressive Model ◽  
The Stability ◽  
Nonlinear Autoregressive

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibility condition.

On stability of nonlinear AR processes with Markov switching

2000 ◽  
Vol 32 (02) ◽  
pp. 394-407 ◽  
Author(s):  
J.-F. Yao ◽  
J.-G. Attali
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Stability Problem ◽  
Law Of Large Numbers ◽  
Markov Switching ◽  
Strong Law ◽  
Large Numbers ◽  
Nonlinear Autoregressive Model ◽  
The Stability ◽  
Nonlinear Autoregressive

We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibility condition.

Introduction

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Phase Transitions ◽  
Statistical Mechanics ◽  
Conservation Laws ◽  
Law Of Large Numbers ◽  
Macroscopic Scale ◽  
Classical Probability ◽  
Large Numbers ◽  
Microscopic World ◽  
New Phenomena

Statistical mechanics concerns the transition from the microscopic to the macroscopic realm. On a macroscopic scale new phenomena arise that have no counterpart in the microscopic world. For example, macroscopic systems have a temperature; they might undergo phase transitions; and their dynamics may involve dissipation. How can such phenomena be explained? This chapter discusses the characteristic differences between the microscopic and macroscopic realms and lays out the basic challenge of statistical mechanics. It suggests how, in principle, this challenge can be tackled with the help of conservation laws and statistics. The chapter reviews some basic notions of classical probability theory. In particular, it discusses the law of large numbers and illustrates how, despite the indeterminacy of individual events, statistics can make highly accurate predictions about totals and averages.

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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