Simulations are often needed when the performance of new methods is evaluated. If the method is designed to be blind or robust, simulation studies must cover the whole range of potential random input. It follows that there is a need for advanced tools of data generation. The purpose of this paper is to introduce a technique for the generation of correlated multivariate random data with non-Gaus...

In this paper, we derive a new version of Hanson–Wright inequality for sparse bilinear form sub-Gaussian variables. Our results are generalization previous deviation inequalities that consider either quadratic forms or dense forms. We apply the concentration to testing cross-covariance matrix when data subject missing. Using our results, can find threshold value correlations controls family-wis...

We show that a-parabolic Harnack inequality for random walks on graphs is equivalent, on one hand, to so called-Gaussian estimates for the transition probability and, on the other hand, to the conjunction of the elliptic Harnack inequality, the doubling volume property, and the fact that the mean exit time in any ball of radius R is of the order R. The latter condition can be replaced by a cert...

The particle swarm optimization (PSO), now widely used in the electromagnetics community, is a robust evolutionary method based on the property of swarm intelligence. This paper focuses on the random variable effect in the PSO algorithm, and two random distribution functions, namely, the uniform distribution and Gaussian distribution, are studied and compared in details. It is revealed through ...

The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates Lp([0, T ]) and uniform approximations of φ-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for wh...

We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index governing the tail heaviness (or jump index) equals the escape time exponent (or walk dimension) of the sub-Gaussian estimate. In a certain sense, this generalize...

We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$ Bernoulli random variable. We analyze an unbiased covariance estimator under this model, and derive an error bound that reveals relations between the sub-sampling...

We derive a dimension-free Hanson–Wright inequality for quadratic forms of independent sub-gaussian random variables in separable Hilbert space. Our is an infinite-dimensional generalization the classical finite-dimensional Euclidean vectors. illustrate application to generalized $K$-means clustering problem non-Euclidean data. Specifically, we establish exponential rate convergence semidefinit...