The inverse of a local operator preserves the Markov property
The irrelevant information principle for collective probabilistic reasoning
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...
The island model as a Markov dynamic system
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators....
The jammed phase of the Biham-Middleton-Levine traffic model.
The joint law of ages and residual lifetimes for two schemes of nested regenerative sets.
The Kendall theorem and its application to the geometric ergodicity of Markov chains
We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of...
The kernel method: a collection of examples.
The Kiefer-Wolfowitz approximation method in controlled Markov chains
The Kolmogorov distance between the binomial and Poisson laws: efficient algorithms and sharp estimates.
The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.
The Kolmogorov equation with time-measurable coefficients.
The Kurzweil-Henstock theory of stochastic integration
The Kurzweil-Henstock approach has been successful in giving an alternative definition to the classical Itô integral, and a simpler and more direct proof of the Itô Formula. The main advantage of this approach lies in its explicitness in defining the integral, thereby reducing the technicalities of the classical stochastic calculus. In this note, we give a unified theory of stochastic integration using the Kurzweil-Henstock approach, using the more general martingale as the integrator. We derive...
The Laplace transform of measures on the cone of a vector lattice.
The large deviation principle for certain series
We study the large deviation principle for stochastic processes of the form , where is a sequence of i.i.d.r.v.'s with mean zero and . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition,...
The large deviation principle for certain series
We study the large deviation principle for stochastic processes of the form , where is a sequence of i.i.d.r.v.’s with mean zero and . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition,...
The large-scale limit of Dyson's hierarchical vector valued model at low temperatures. The non-gaussian case. Part I : limit theorem for the average spin
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit
The largest component in an inhomogeneous random intersection graph with clustering.
The LASSO estimator: Distributional properties
The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of orthogonal models....
The law of exponential decay for r-adic transformations