scholarly journals Large deviations for a class of tempered subordinators and their inverse processes

2021 ◽  
pp. 1-21
Author(s):  
Nikolai Leonenko ◽  
Claudio Macci ◽  
Barbara Pacchiarotti
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Large Deviation ◽  
Common Law ◽  
Random Variables ◽  
Tempered Distributions ◽  
One Dimensional ◽  
Large Deviation Principles ◽  
Time Changes ◽  
Non Gaussian

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate deviations result. More precisely we mean a class of large deviation principles that fill the gap between the (trivial) weak convergence of some non-Gaussian identically distributed random variables to their common law, and the convergence of some other related random variables to a constant. Some other minor results concern large deviations for the inverse of the tempered subordinators considered in this paper; actually, in some results, these inverse processes appear as random time-changes of other independent processes.

A large deviations heuristic made precise

2000 ◽  
Vol 128 (3) ◽  
pp. 561-569 ◽  
Author(s):  
NEIL O'CONNELL
Keyword(s):  
Large Deviations ◽  
Bin Packing ◽  
Symmetric Functions ◽  
Large Deviation ◽  
Random Variables ◽  
Packing Problem ◽  
Rate Function ◽  
Empirical Measures ◽  
Underlying Distribution ◽  
Uniformly Lipschitz

Sanov's Theorem states that the sequence of empirical measures associated with a sequence of i.d.d. random variables satisfies the large deviation principle (LDP) in the weak topology with rate function given by a relative entropy. We present a derivative which allows one to establish LDPs for symmetric functions of many i.d.d. random variables under the condition that (i) a law of large numbers holds whatever the underlying distribution and (ii) the functions are uniformly Lipschitz. The heuristic (of the title) is that the LDP follows from (i) provided the functions are ‘sufficiently smooth’. As an application, we obtain large deviations results for the stochastic bin-packing problem.

LARGE DEVIATIONS FOR SMALL PERTURBATIONS OF SDES WITH NON-MARKOVIAN COEFFICIENTS AND THEIR APPLICATIONS

2006 ◽  
Vol 06 (04) ◽  
pp. 487-520 ◽  
Author(s):  
FUQING GAO ◽  
JICHENG LIU
Keyword(s):  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Wiener Space ◽  
Small Perturbations ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
Sobolev Norms

We prove large deviation principles for solutions of small perturbations of SDEs in Hölder norms and Sobolev norms, where the SDEs have non-Markovian coefficients. As an application, we obtain a large deviation principle for solutions of anticipating SDEs in terms of (r, p) capacities on the Wiener space.

scholarly journals Nonstandard limit theorems and large deviations for the Jacobi beta ensemble

2014 ◽  
Vol 03 (03) ◽  
pp. 1450012 ◽  
Author(s):  
Jan Nagel
Keyword(s):  
Weak Convergence ◽  
Spectral Measure ◽  
Limit Theorems ◽  
Large Deviation ◽  
The Other ◽  
Limit Measure ◽  
Jacobi Ensemble ◽  
Large Deviation Principles ◽  
Beta Ensemble ◽  
Rate Functions

In this paper, we show weak convergence of the empirical eigenvalue distribution and of the weighted spectral measure of the Jacobi ensemble, when one or both parameters grow faster than the dimension n. In these cases, the limit measure is given by the Marchenko–Pastur law and the semicircle law, respectively. For the weighted spectral measure, we also prove large deviation principles under this scaling, where the rate functions are those of the other classical ensembles.

scholarly journals Large deviations for stochastic integrodifferential equations of the Itô type with multiple randomness

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 473-487 ◽  
Author(s):  
A. Haseena ◽  
M. Suvinthra ◽  
N. Annapoorani
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Finite Number ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Integrodifferential Equations ◽  
Multiplicative Noises ◽  
Deviation Principle ◽  
Laplace Principle ◽  
Weak Convergence Approach

A Freidlin-Wentzell type large deviation principle is derived for a class of It? type stochastic integrodifferential equations driven by a finite number of multiplicative noises of the Gaussian type. The weak convergence approach is used here to prove the Laplace principle, equivalently large deviation principle.

scholarly journals Large deviations for exchangeable observations with applications

2004 ◽  
Vol 2004 (55) ◽  
pp. 2947-2958
Author(s):  
Jinwen Chen
Keyword(s):  
Large Deviations ◽  
Large Deviation ◽  
Random Variables ◽  
Moment Conditions

We first prove some large deviation results for a mixture of i.i.d. random variables. Compared with most of the known results in the literature, our results are built on relaxing some restrictive conditions that may not be easy to be checked in certain typical cases. The main feature in our main results is that we require little knowledge of (continuity of) the component measures and/or of the compactness of the support of the mixing measure. Instead, we pose certain moment conditions, which may be more practical in applications. We then use the large deviation approach to study the problem of estimating the component and the mixing measures.

Large deviations for the stochastic predator–prey model with nonlinear functional response

2017 ◽  
Vol 54 (2) ◽  
pp. 507-521 ◽  
Author(s):  
M. Suvinthra ◽  
K. Balachandran
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Functional Response ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Solution Processes ◽  
Prey Model

AbstractIn this paper we consider a diffusive stochastic predator–prey model with a nonlinear functional response and the randomness is assumed to be of Gaussian nature. A large deviation principle is established for solution processes of the considered model by implementing the weak convergence technique.

scholarly journals Large deviation principles of one-dimensional maps for Hölder continuous potentials

2014 ◽  
Vol 36 (1) ◽  
pp. 127-141 ◽  
Author(s):  
HUAIBIN LI
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Weak Form ◽  
Periodic Points ◽  
Hölder Continuous ◽  
One Dimensional ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
One Dimensional Maps ◽  
Level 2

We show some level-2 large deviation principles for real and complex one-dimensional maps satisfying a weak form of hyperbolicity. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages.

scholarly journals Cramér type large deviations for trimmed L-statistics

2018 ◽  
Vol 37 (1) ◽  
pp. 101-118 ◽  
Author(s):  
Nadezhda Gribkova
Keyword(s):  
Large Deviations ◽  
Weight Function ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Natural Conditions ◽  
New Approach ◽  
Probabilities Of Large Deviations ◽  
Large Deviation Problem ◽  
Deviation Problem

CRAMÉR TYPE LARGE DEVIATIONS FOR TRIMMED L-STATISTICSIn this paper, we propose a new approach to the investigationof asymptotic properties of trimmed L-statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. 1982 – the first and, as far as we know, the single article where some results on probabilities of large deviations for the trimmed L-statistics were obtained, but under some strict and unnatural conditions. Our approach is to approximate the trimmed L-statistic by a non-trimmed L-statistic with smooth weight function based onWinsorized random variables. Using this method, we establish the Cramér type large deviation results for the trimmed L-statistics under quite mild and natural conditions.

Large deviations for departures from a shared buffer

1997 ◽  
Vol 34 (3) ◽  
pp. 753-766 ◽  
Author(s):  
Neil O'connell
Keyword(s):  
Large Deviations ◽  
Large Deviation ◽  
The State ◽  
Stationary Case ◽  
Service Capacity ◽  
Equilibrium System ◽  
Large Deviation Principles ◽  
Service Policy ◽  
Shared Buffer

In this paper we describe how the joint large deviation properties of traffic streams are altered when the traffic passes through a shared buffer according to a FCFS service policy with stochastic service capacity. We also consider the stationary case, proving large deviation principles for the state of the system in equilibrium and for departures from an equilibrium system.

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