Inequalities for sums of independent geometrical random variables.
Inequalities for the ergodic maximal function
Inequalities for the moments and distribution of the ladder height of a random walk.
Inequalities for Walsh like random variables.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Inequalities relative to two-parameter Vilenkin-Fourier coefficients
Inequality of two critical probabilities for percolation.
Inéquations quasi variationnelles dépendant d'un paramètre
Inference on the variance and smoothing of the paths of diffusions
Inferring the residual waiting time for binary stationary time series
For a binary stationary time series define to be the number of consecutive ones up to the first zero encountered after time , and consider the problem of estimating the conditional distribution and conditional expectation of after one has observed the first outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state...
Infimum-convolution description of concentration properties of product probability measures, with applications
Infinite dimensional Gegenbauer functionals
he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
Infinite dimensional stationary sequences with multiplicity one. II.
Infinite divisibility of Gaussian squares with non-zero means.
Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
We first characterize the increasing eigenfunctions associated to the following family of integro-differential operators, for any α, x>0, γ≥0 and fa smooth function on , where the coefficients ,σ≥0 and the measure ν, which satisfies the integrability condition ∫0∞(1∧r2)ν(dr)<+∞, are uniquely determined by the distribution of a spectrally negative, infinitely divisible random variable, with characteristic exponent ψ. L(γ) is known to be the infinitesimal generator of a positive...
Infinite invariant measures for non-uniformely expanding transformations of [0, 1]: weak law of large numbers with anamalous scaling.
Infinite paths and cliques in random graphs
We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.
Infinite probabilistic secret sharing
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms. A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share...
Infinite products of random matrices and repeated interaction dynamics
Let Ψn be a product of n independent, identically distributed random matrices M, with the properties that Ψn is bounded in n, and that M has a deterministic (constant) invariant vector. Assume that the probability of M having only the simple eigenvalue 1 on the unit circle does not vanish. We show that Ψn is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as n→∞. The fluctuating part converges in Cesaro mean to a limit that is characterized...
Infinite pseudo-random sequences of high algorithmic complexity