Search Results - (Author, Cooperation:S. Carmona)

2018-03-23

The American Society for Microbiology (ASM)

0019-9567

1098-5522

Medicine

2016-03-19

American Association for the Advancement of Science (AAAS)

0036-8075

1095-9203

Biology

Chemistry and Pharmacology

Computer Science

Medicine

Natural Sciences in General

Physics

Aging/immunology ; Amyotrophic Lateral Sclerosis/genetics/*immunology ; Animals ; Frontotemporal Dementia/genetics/*immunology ; Gene Knockdown Techniques ; Guanine Nucleotide Exchange Factors/genetics/*physiology ; Heterozygote ; Humans ; Lymphatic Diseases/genetics/immunology ; Macrophages/*immunology ; Mice ; Mice, Knockout ; Microglia/*immunology ; Myeloid Cells/*immunology ; Proteins/genetics/*physiology ; Rats ; Splenomegaly/genetics/immunology

2018-07-24

The American Society for Microbiology (ASM)

0019-9567

1098-5522

Medicine

1572-9613

Large deviation ; level 1 entropy function ; level 2 entropy function ; contraction principle ; ergodic transformations ; Markov process

Springer Online Journal Archives 1860-2000

Physics

Abstract A large-deviation principle (LDP) at level 1 for random means of the type $$M_n \equiv \frac{1}{n}\sum\limits_{j = 0}^{n - 1} {Z_j Z_{j + 1} ,{\text{ }}n = 1,2,...}$$ is established. The random process {Z n} n≥0 is given by Z n = Φ(X n) + ξ n , n = 0, 1, 2,..., where {X n} n≥0 and {ξ n} n≥0 are independent random sequences: the former is a stationary process defined by X n = T n(X 0), X 0 is uniformly distributed on the circle S 1, T: S 1 → S 1 is a continuous, uniquely ergodic transformation preserving the Lebesgue measure on S 1, and {ξn} n≥0 is a random sequence of independent and identically distributed random variables on S 1; Φ is a continuous real function. The LDP at level 1 for the means M n is obtained by using the level 2 LDP for the Markov process {V n = (X n, ξ n , ξ n+1)} n≥0 and the contraction principle. For establishing this level 2 LDP, one can consider a more general setting: T: [0, 1) → [0, 1) is a measure-preserving Lebesgue measure, $$\Phi :\left[ {0,\left. 1 \right)} \right. \to \mathbb{R}$$ is a real measurable function, and ξ n are independent and identically distributed random variables on $$\mathbb{R}$$ (for instance, they could have a Gaussian distribution with mean zero and variance σ2). The analogous result for the case of autocovariance of order k is also true.

Electronic Resource

1572-9613

level-2 large deviations ; expanding maps ; Gibbs states ; entropy ; Markov process ; additive white noise

Springer Online Journal Archives 1860-2000

Physics

Abstract Large-deviations estimates for the autocorrelations of order kof the random process Z n=φ(X n)+ξ n, n≥0, are obtained. The processes (X n) n≥0and (ξ n) n≥0are independent, ξ n, n≥0, are i.i.d. bounded random variables, X n=T n(X 0), n∈ $$\mathbb{N}$$ , T: M→Mis expanding leaving invariant a Gibbs measure on a compact set M, and φ: M→ $$\mathbb{R}$$ is a continuous function. A possible application of this result is the case where Mis the unit circle and the Gibbs measure is the one absolutely continuous with respect to the Lebesgue measure on the circle. The case when Tis a uniquely ergodic map was studied in Carmona et al.(1998). In the present paper Tis an expanding map. However, it is possible to derive large-deviations properties for the autocorrelations samples (1/n) ∑ n−1 j=0 Z j Z j+k . But the deviation function is quite different from the uniquely ergodic case because it is necessary to take into account the entropy of invariant measures for Tas an important information. The method employed here is a combination of the variational principle of the thermodynamic formalism with Donsker and Varadhan's large-deviations approach.

Electronic Resource