Related papers: Tail Measures and Regular Variation

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

Let $\mathbf{\eta}$ be a positive Radon measure on the space of continuous paths from R into a locally compact Polish space $Y$, and assume that $\mathbf{\eta}$ admits an invariant measure. We explicit conditions on $\mathbf{\eta}$ such…

We consider solutions to so-called stochastic fixed point equation $R \stackrel{d}{=} \Psi(R)$, where $\Psi $ is a random Lipschitz function and $R$ is a random variable independent of $\Psi$. Under the assumption that $\Psi$ can be…

For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…

Skorokhod's J1 and M1 topologies are standard tools in proving limit theorems for stochastic processes. Motivated by applications, we extend these topologies so that they are capable of describing the convergence of a sequence of functions…

Given a Radon probability measure $\mu$ supported in $\mathbb{R}^d$, we are interested in those points $x$ around which the measure is concentrated infinitely many times on thin annuli centered at $x$. Depending on the lower and upper…

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…

Topology change in Lorentzian quantum gravity demands geometric regulators that control curvature, spin structure, and chirality during nontrivial interpolations. We develop a framework for regulated topology change based on smooth…

We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…

Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…

We classify the invariant Borel measures for adic transformations, where the alphabets have bounded size and the measure is finite on the path space of some sub-Bratteli diagram. We develop a nonstationary version of the Frobenius normal…

In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…

Thimble regularization as a solution to the sign problem has been successfully put at work for a few toy models. Given the non trivial nature of the method (also from the algorithmic point of view) it is compelling to provide evidence that…

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…

Optical polarimeters are typically calibrated using measurements of stars with known and stable polarization parameters. However, there is a lack of such stars available across the sky. Many of the currently available standards are not…

Faraday Rotation Measure (RM) Synthesis, as a method for analyzing multi-channel observations of polarized radio emission to investigate galactic magnetic fields structures, requires the definition of complex polarized intensity in the…

For an infinite system of particles arriving in and departing from a habitat $X$ -- a locally compact Polish space with a positive Radon measure $\chi$ -- a Markov process is constructed in an explicit way. Along with its location $x\in X$,…

Lorentz Violation (LV) is posited as a possible relic effect of quantum gravity at low energy scales. The Standard-Model Extension provides an effective field-theoretic framework for examining possible deviations attributed to LV. With…