Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLocal limit theorems for smoothed Bernoulli and other convolutions
62
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
rate research
Read More
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
In this paper, we propose a new interpretation of local limit theorems for univariate and multivariate distributions on lattices. We show that - given a local limit theorem in the standard sense - the distributions are approximated well by the limit distribution, uniformly on intervals of possibly decaying length. We identify the maximally allowable decay speed of the interval lengths. Further, we show that for continuous distributions, the interval type local law holds without any decay speed restrictions on the interval lengths. We show that various examples fit within this framework, such as standardized sums of i.i.d. random vectors or correlated random vectors induced by multidimensional spin models from statistical mechanics.
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough path techniques. As a by-product, we provide a natural explanation of the various new asymptotic behaviors in contrast with the classical unweighted random sum case. We apply our principle to derive some weighted type Breuer-Major theorems, which generalize previous results to random sums that do not have to be in a finite sum of chaos. In this context, a Breuer-Major type criterion in notion of Hermite rank is obtained. We also consider some applications to realized power variations and to Itos formulas in law. In the end, we study the asymptotic behavior of weighted quadratic variations for some multi-dimensional Gaussian processes.
In this paper we consider some non linear Hawkes processes with signed reproduction function (or memory kernel) thus exhibiting both self-excitation and inhibition. We provide a Law of Large Numbers, a Central Limit Theorem and large deviation results, as time growths to infinity. The proofs lie on a renewal structure for these processes introduced in Costa et al. (2020) which leads to a comparison with cumulative processes. Explicit computations are made on some examples. Similar results have been obtained in the literature for self-exciting Hawkes processes only.
We derive herein the limiting laws for certain stationary distributions of birth-and-death processes related to the classical model of chemical adsorption-desorption reactions due to Langmuir. The model has been recently considered in the context of a hybridization reaction on an oligonucleotide DNA microarray. Our results imply that the truncated gamma- and beta- type distributions can be used as approximations to the observed distributions of the fluorescence readings of the oligo-probes on a microarray. These findings might be useful in developing new model-based, probe-specific methods of extracting target concentrations from array fluorescence readings.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
