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We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distance...
Research in a number of fields now requires the analysis of "multi-block" data, in which multiple high-dimensional, and fundamentally disparate, datatypes are available for a common set of objects. In...
Research in a number of fields now requires the analysis of "multi-block" data, in which multiple high-dimensional, and fundamentally disparate, datatypes are available for a common set of objects. In...
We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint...
We study the problem of estimating parameters of the limiting equation of a multiscale diffusion in the case of averaging and homogenization, given data from the corresponding multiscale system. Fir...
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on E = [0,1]d\{(0, 0, · · · , 0)} and models another regular variation on the sub-cone E(2) = E...
We study continuous additive functionals of zero quadratic variation of strong Markov continuous local martingales by means of stochastic calculus. We show that they admit a representation as a sto...
For strictly stationary random sequences satisfying the "minimal" dependence condition, necessary and sufficient conditions for the weak convergence to the normal law in terms of slow variation in ...
In this note, we are interested in the regularity in the sense of total variation of the joint laws of multiple stable stochastic integrals. Namely, we show that the convergence L 􀀀 Id1 ...
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose va...
A recent theorem by M. Manstavicius (2004) provided a link between a certain function of transition probabilities of a strong Markov process and the boundedness of the p-variation of its trajectories....
A recent theorem by M. Manstavicius (2004) provided a link between a certain function of transition probabilities of a strong Markov process and the boundedness of the p-variation of its trajectories....
An important tool to quantify the likeness of two probability measures are f–divergences, which have seen widespread application in statistics and information theory. An example is the total variati...
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain...

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