Large deviation principles for random measures

  • 73 Pages
  • 1.28 MB
  • 3885 Downloads
  • English
by
Measure theory., Large deviations., Poisson proce
Statementby Dae-sik Hwang.
The Physical Object
Pagination73 leaves, bound :
ID Numbers
Open LibraryOL15194240M

These large deviation principles have been discovered for independent and identically distributed random variables, as well as random vectors and these have been extended to some cases of weak dependence.

In this thesis we prove large deviation principles for finite dimensional distributions of scaling limits of random : Daesik Hwang.

We succeed in proving the large deviation principle for a large class of measures with random weights and obtaining the corresponding rate function in an explicit form.

In particular, our results are applicable to the Fermi gas and the spherical by: 9. large deviation principle for the empirical neighborhood measure and the empirical pair measure of a colored random graph in the weak topology; see Theorem In the course of the proof of this principle, two further interesting large deviation principles are established: a large deviation principle for the empirical neighbor.

pair measure of a coloured random graph in the weak topology, see Theorem In the course of the proof of this principle, two further interesting large deviation principles are established: A large deviation principle for the empirical neighbourhood measure conditioned to have a given empirical pairCited by: To formulate the large deviation principle, we call a pair of measures (̟,ν)∈M˜(X ×X)×M(X ×N(X)) sub-consistent if (1) hν(,ℓ),ℓ()i(a,b) ≤̟(a,b) for all a,b∈X, LARGE DEVIATION PRINCIPLES FOR COLORED RANDOM GRAPHS5 and consistent if equality holds in (1).

Large deviation principles for empirical measures of the multitype random networks. 03/22/ ∙ by K. Doku-Amponsah, et al. ∙ University of Ghana ∙ 0 ∙ share.

In this article we study the stochastic block model also known as the multi-type random networks (MRNs). Gantert N. () Large Deviation Principles for Random Fields on a Binary Tree.

In: Chauvin B., Cohen S., Rouault A. (eds) Trees. Progress in Probability, vol Large deviation principles for empirical measures of coloured random graphs.

By Kwabena Doku-amponsah. Abstract. Unfortunately we have to report a mistake in the paper with the above title, published Large deviation principles for random measures book [2]. The proof of the lower bound for the large deviation probabilities in Theoremgiven in Sectionrequires the pair (̟, ν) to be.

Large deviation principles are proved for rescaled Poisson random measures. As a consequence, Freidlin–Wentzell type large deviations results for processes with independent increments are obtained in situations where exponential moments are infinite.

Empirical Measures on Multitype Random Networks; Doku-Amponsah (). Statement and Discussion of Results. Further Work Hellman and Staudigl() Kwabena Doku-Amponsah DFD-AIMS WORKSHOP ON EVOLUTIONN PROCESSES ON NETWORKS, ANDRWA-KIGALI, MARCHLARGE DEVIATION PRINCIPLES FOR EMPIRICAL MEASURES OF MULTITYPE RANDOM.

The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events.

Details Large deviation principles for random measures PDF

The abstract theory of large deviation principles plays more or less the same role as measure theory in (usual) probability theory. On the other hand, there is a much richer and much more important side of large deviation theory, which tries to identify rate functions Ifor various functions Fof independent random variables, and study their.

The book is bound to become the standard reference on the subject.” (Frank Aurzada, Mathematical Reviews, June, ) “This book deals with a different aspects of the theory of random measures. this is a useful book for a researcher in probability theory and mathematical statistics.

Understanding that large deviation principles provide a bridge between probability and analysis (PDEs, convex and variational analysis).

Large deviation theory as the mathematical foundation of mathematical statistical mechanics (Gibbs measures; free energy calculations; entropy-energy competition). Abstract In this paper, we establish a large deviation principle for a mean reflected stochastic differential equation driven by both Brownian motion and Poisson random measure.

For a class of models of sparse coloured random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degree distribution of Erdos-Renyi.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Unfortunately we have to report a mistake in the paper with the above title, published in [2]. The proof of the lower bound for the large deviation probabilities in Theoremgiven in Sectionrequires the pair (̟, ν) to be consistent rather than only sub-consistent.

For suitably defined empirical measures of a class of models of sparse coloured random graphs, we prove large deviation principles,with rate functions explicitly expressed in terms of relative entropies, in the weak topology.

Download Large deviation principles for random measures EPUB

They conclude with the LDP for the empirical measure of (discrete time) random processes: Sanov's theorem for the empirical measure of an i.i.d. sample, its extensions to Markov processes and mixing sequences and their application. The present soft cover edition is a corrected printing of the edition.

We prove large deviation principles for Poisson random measures and an implicit contraction principle. These results are applied to provide a large deviation principle for a maximum likelihood estimator in a parametric statistical model and to explicitly identify the rate function.

The main aim of this project is to define suitable empirical measures of the d -regular random graphs, and hence prove Large deviation principles for the empirical measures. The function Iis called the rate function for the large deviation principle. A rate function Iis called a good rate function if for each a2[0;1) the level set fx: I(x) agis compact.

The traditional approach to large deviation principles is via the so-called change of measure method. For a class of models of sparse coloured random graphs, we prove large deviation principles for these empirical measures in the weak topology.

The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. There are plenty of classical books about large deviation techniques. Here are two: Dembo and Zeitouni – Large deviation techniques and applications.

It is quite successful, with more that citations for the three editions on Mathscinet to date. Dupuis and Ellis – A weak convergence approach to the theory of large deviations.

Contraction principle (large deviations theory), a result on how large deviations principles " push forward " Freidlin–Wentzell theorem, a large deviations principle for Itō diffusions Laplace principle, a large deviations principle in Rd. Downloadable (with restrictions).

We consider the parametric estimation problem of intensity measure of a Poisson random measure. We prove large deviation principles for Poisson random measures and an implicit contraction principle. These results are applied to provide a large deviation principle for a maximum likelihood estimator in a parametric statistical model and to explicitly identify.

Here Bis a set of probabilistic vectors (empirical measures) in a (suitable) Euclidean space (R‘ or R‘2 and so on); the form of Bdepends upon the choice of sets B n. (Set Bis constructed from a frequency analysis of strings xn 1 0 2B n and turns out to be a convex polyhedron.) Next, is a large deviation rate (LDR) function.

Typically.

Description Large deviation principles for random measures PDF

The present paper is a continuation of [A. Borovkov and A. Mogulskii, Theory Probab. Appl., 56 (), pp. It consists of three sections. Section 3 presents an example showing that it is necessary to extend the problem setup and the very concept of the “large deviations principle” (l.d.p.).

We introduce a new, extended function space, a metric in it, and a deviation. Large Deviation Theory allows us to formulate a variant of () that is well-de ned and can be established rigorously.

The point is that if we take a small Brownian trajectoryp "x() and force it to be near a given y2, then for y6= 0 this is a rare event and the energy of such trajectory is so large that dominates the probability of its.

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of a class of models of sparse colored random graphs, we prove large deviation principles for these empirical.

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors.

For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical.In this paper, we establish the local large deviation principle (LLDP) for the Wiener processes with random resettings, where the resettings occur at the arrival time of a Poisson process.

Here, at each resetting time, a new resetting point is selected at random, according to a conditional distribution.For a general overview we refer to the books of Anderson et al. (), Forrester () and Mehta (). For the weighted random measure, large deviation principles were proven by Gamboa and Rouault (, ) and central limit theorems can be found in the papers of Lytova and Pastur (a,b) and Dette and Nagel ().