An algorithm for the distribution of the time between coincidences of two independent PH-renewal processes
An almost sure central limit theorem for independent random variables
An almost sure invariance principle for renormalized intersection local times.
An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law
We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.
An almost sure limit theorem for the maxima of strongly dependent Gaussian sequences.
An almost sure limit theorem for -mixing random fields.
An Alpern tower independent of a given partition
Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.
An alternative proof of a theorem of Aldous concerning convergence in distribution for martingales
An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes
P. Samek and D. Volný, in the paper ``Uniqueness of a martingale-coboundary decomposition of a stationary processes" (1992), showed the uniqueness of martingale-coboundary decomposition of strictly stationary processes. The original proof is given by reducing the problem to the ergodic case. In this note we give another proof without such reduction.
An American convert close to maturity.
An analog of Wald's identity for random walks with infinite mean.
An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations
We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...
An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations
We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...
An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem
We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.
An analytical characterization for an optimal change of Gaussian measures.
An application of a functional equation to information theory
An application of -condition in the theory of stochastic differential equations
An application of Markov operators in differential and integral equations
An application of matrix calculus to an engineering problem.