A Lognormal Central Limit Theorem for Particle Approximations of ...
Recommend Documents
Jul 24, 2012 - Bernoulli trials and, in some cases, also for Markov-dependent trials. ... for success and failure runs of various lengths with Bernoulli trials that ...
Fu [9] studied multi-state trials by examining the joint distribution of runs and ... for Markov dependent binary trials, showed that it obeys a multivariate CLT and ...
Theorem 3.1 generalizes the Hoeffding inequality and improves results of Talagrand [14] in the case of symmetric Bernoulli variables. Next we prove that. (2).
The present analysis is concerned with genetic-type interacting particle systems. ... dom particle systems to solve the filtering problem numerically. That particle.
cerned with genetic-type interacting particle systems. Our aim is to ... The random particle system (; Fn;( n)n 0; P) associated to (2) will be a. Markov process with ...
The main result of this paper is a general central limit theorem for distributions defined ...... where Qr are the so called Edgeworth polynomials. They are formal ...
variance, Ï2, distribute normally with mean, μ, and variance, Ï2 n . Using the .... distribution of the population does not affect the distribution of the sample .... tized distribution of the sample means is equal to the Student's t- distribution
CENTRAL LIMIT THEOREM HANDOUT. SYMBOLS s sample standard deviation s. 2 sample variance Ï population standard deviation
Sn = X1 +X2 +···+Xn. Then Sn is the number of successes in n trials. We know ..... pieces of apple pie ordered on a g
The Gallup Poll has used these polling techniques in every Presidential election since 1936 (and in innumerable ...... t
that Sn has as its distribution the binomial probabilities b(n, p, j). ... S. ∗ n always
has expected value 0 and variance 1. 2. Suppose we plot a spike graph with ...
California at Los Angeles, written under Professor Charles J. Stone. ... applications of Rosen's theorem involves the above-mentioned limit theorems, and ...
In this. Received May 2005; revised September 2005. 1Supported in part by a Charles Phelps Taft Memorial Fund Grant and NSA Grant. H98230-05-01-0066.
Jan 14, 2014 - that given m, n there are exactly two vertices with co- .... the graph so obtained is “quasi-periodic” (or periodic if the angles of the triangle ∆ are ...
P. Billingsley. Convergence of Probability Measures. Wiley, New York, 1968. 4. A. Borodin, A. Okounkov, and G. Olshanski. Asymptotics of Plancherel measures.
sullo spazio di Fock Booleano a mezzo di un teorema di limite centrale quantistico ... in [16] the *-algebra and the state are the same either for the convergent.
Dec 11, 2015 - PR] 11 Dec 2015 ... December 14, 2015 ... have applications in various branches of science, e.g. in medicine [1, 23], in geostatistics [5, 25] or.
Jul 18, 2018 - called Clebsch-Gordan coefficients (see [36], [16]), which arise from integrals of multiple ...... In the table and the graphs below, we compare br.
Apr 21, 2014 - Since u0 s(y) is a PDE then the integrand in Ito integral (16) is deterministic. 9 .... I am also thankful to Dr. Kei Kobayashi for pointing.
May 9, 2010 - of blocks of random variables separated by a certain time gap and called ... of stationary random variables and by Theorem 1 in Coulon-Prieur ...
des produits au sens max-plus. Ph.D. thesis, Univ. Rennes. Available at http://tel.ccsd.cnrs.fr/tel-00010813. [30] Resing, J. A. C., de Vries, R. E., Hooghiemstra, G.
Abstract. The global Lyapunov exponent of a dynamical system measures the long ... short-term growth rates that can be identified in local regions (Bailey, Ellner & Ny- ...... Probability and Measure, John Wiley & Sons, Inc., New York. Doob ...
which all random variables are defined. ... In § 1 and § 2 we show that the random variable ... In order to state our results, we shall introduce some notations.
Oct 1, 2014 - PR] 1 Oct 2014. ON A CENTRAL LIMIT THEOREM FOR. SHRUNKEN WEAKLY DEPENDENT. RANDOM VARIABLES. Richard C. Bradleyâ ...
A Lognormal Central Limit Theorem for Particle Approximations of ...
Jun 30, 2013 - One then has the following convergence in distribution: log γN n (1) d ... exhibits a log-normal distribution. ..... is a Cauchy sequence, so that Φ.
A Lognormal Central Limit Theorem for Particle Approximations of Normalizing Constants Jean B´erard∗, Pierre Del Moral†, Arnaud Doucet‡
arXiv:1307.0181v1 [math.PR] 30 Jun 2013
July 22, 2013
Abstract This paper deals with the numerical approximation of normalizing constants produced by particle methods, in the general framework of Feynman-Kac sequences of measures. It is well-known that the corresponding estimates satisfy a central limit theorem for a fixed time horizon n as the number of particles N goes to infinity. Here, we study the situation where both n and N go to infinity in such a way that limn→∞ n/N = α > 0. In this context, Pitt et al. [11] recently conjectured that a lognormal central limit theorem should hold. We formally establish this result here, under general regularity assumptions on the model. We also discuss special classes of models (time-homogeneous environment and ergodic random environment) for which more explicit descriptions of the limiting bias and variance can be obtained. Keywords : Feynman-Kac formulae, mean field interacting particle systems, particle free energy models, nonlinear filtering, particle absorption models, quasi-invariant measures, central limit theorems. Mathematics Subject Classification : Primary: 65C35, 47D08, 60F05; Secondary: 65C05, 82C22, 60J70.
1
Introduction
1.1
Feynman-Kac measures and their particle approximations
Consider a Markov chain (Xn )n≥0 on a measurable state space (E, E), whose transitions are prescribed by a sequence of Markov kernels (Mn )n≥1 , and a collection of positive bounded and measurable functions (Gn )n≥0 on E. We associate to (Mn )n≥1 and (Gn )n≥0 the sequence of unnormalized Feynman-Kac measures (γn )n≥0 on E, defined through their action on bounded (real-valued) measurable functions by: Y γn (f ) := E f (Xn ) Gp (Xp ) . (1.1) 0≤p
