Limit theorems (Probability theory)
Eventologically multivariate extensions of probability theory’s limit theorems
... When number of tests n is large, calculating of binomial as in univariate and in multivariate versions may be a trouble. Therefore search of asymptotic formulas for these probabilities when n → ∞ is important task. ...
6
Limit theorems leading to Bose Einstein, Maxwell Boltzmann statistics and Zipf Mandelbrot law
... the limit theorems. The branch of Mathematics which deals with limit theorems is Probability Theory, hence these are probabilistic ...of limit theo- rems, Bose-Einstein and ...
169
On the rate of convergence in limit theorems for random sums via Trotter distance
... of limit theorems for sums of independent random variables (the interested reader is referred to the results of Zolotarev [] and [], Kirschfink [], Kalashnikov [], Hung in [] and ...
12
A note on the almost sure central limit theorems for the maxima and sums
... where, here and in the sequel, I(A) is the indicator function of the event A and (x) stands for the standard normal distribution function. This result was firstly proved independently by Brosamler [] and Schatte [] ...
8
Some limit theorems for ratios of order statistics from uniform random variables
... A: Limit theorems for arrays of ratios of order ...A: Limit theorems for order statistics from ...X: Limit properties for ratios of order statistics from ...Various limit ...
18
Almost sure central limit theorems for strongly mixing and associated random variables
... In this paper, we prove almost sure limit theorems which generalize Theorems 1.1 and 1.2. We also show that under the stationarity assumption, Theorems 1.4 and 1.6 imply Theorems 1.1 ...
7
Limit theorems for weighted samples with applications to sequential Monte Carlo methods
... knowledge, limit theorems for such weighted approximations were only considered in [11], who mostly sketched consistency ...central limit theorems, under assumptions that are presumably closed ...
7
Fluctuation limit theorems for age-dependent critical binary branching systems
... no longer a Markov process. Another striking difference with respect to the case of exponential lifetimes arises when the particle lifetime distribution satisfies (1): heavy-tailed lifetimes enhance the mobility of ...
18
Basic Limit Theorems for Light Traffic Queues & Their Applications
... Limit theorems over the years such as the ones used in this note, have been developed for various queuing models to show limiting behavior. For instance, on light traffic models, the series of deterministic ...
12
Limit theorems and inequalities via martingale methods
... Let us barely mention some obervables to which we can apply the previous inequalities sucessfully. More details can be found in Collet, Martinez and Schmitt (2000), Chazottes, Collet and Schmitt (2005b) and Chazottes and ...
20
Limit theorems for ratios of order statistics from uniform distributions
... classical limit properties, such as the law of iterated logarithm, do not ...the limit theorems for self-normalized sum usually require much less stringent moment conditions than the classical ...
14
Central limit theorems for the real eigenvalues of large Gaussian random matrices
... Finally, as noted in [9], the real eigenvalues of Ginibre matrices bare a close analogy to the study of real roots of random polynomials of high degree. For a quite general class of random polynomials, variance estimates ...
16
Central limit theorems for the spectra of classes of random fractals
... central limit theorem which captures the fluctuations around this ...central limit theorem describing the fluctuations about this, though the positivity of the variance arising in the central limit ...
42
Applications of Malliavin Calculus to Limit Theorems
... In this chapter we examine the limits of partial sum processes. The general setup is described in Section 4.1. The limit theorems discussed here can be viewed as a general- ization of Donsker’s theorem to ...
92
Some limit theorems for the log optimal portfolio
... limit theorems for independent and identically distributed ...strong limit theorems for ar- bitrary random variables and the strong law of large numbers for the ∗ -mixing ...some limit ...
10
Limit Theorems on Fuzzy Markov Chains
... The theory of Markov systems provide an effective and powerful tool for describing State of the system. Since numerous applied probability models can be adopted in their framework. Roughly speaking the Markov property ...
7
Limit theorems for a random directed slab graph
... distance between the two integers. Under broad conditions, we identify a regenerative structure that enables us to prove limit theorems for the maximal path length in a long chunk of the graph. The model is ...
26
Limit Theorems of Integrals with Respect to Vector Random Measures in Complete Paranormed Spaces
... Abstract: This paper studies random integral of the form ∫ gdM , where f is a function taking value in a paranormed vector space X, and M is an independent scattered vector random measure. Random integrals of this type ...
6
Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees
... In this section, we mainly consider a controlled tree, which is a non-uniformly bounded- degree tree with assumption () holding. Theorem and Theorem give two kinds of strong limit theorems for ...
9
Limit theorems for sums of random exponentials
... classical limit theorems concerning the bulk of the sample, ...Central Limit Theorem (CLT), on the one hand, and limit theorems for extreme values, on the other ...
34