Related papers: Russo's formula for random interlacements
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
Original paper: We revisit the probability that any two consecutive events in a Poisson process N on [0,t] are separated by a time interval which is greater than s(<t) (a particular scan statistic probability), and the closely related…
Cranley and Patterson put forward the following randomization as the basis for the estimation of the error of a lattice rule for an integral of a one-periodic function over the unit cube in s dimensions. The lattice rule is randomized using…
We investigate higher derivative estimates for the Lam\'e system with hard inclusions embedded in a bounded domain in $\mathbb{R}^{d}$. As the distance $\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
The `classical' model for a massive spinning particle, which was recently proposed, is derived from the isotropic rotator model. Through this derivation, we note that the spin can be understood as the relativistic extension of the isotropic…
In recent years, there has been an increased need for the use of active systems - systems required to act automatically based on events, or changes in the environment. Such systems span many areas, from active databases to applications that…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
Let $X$ be the number of $k$-term arithmetic progressions contained in the $p$-biased random subset of the first $N$ positive integers. We give asymptotically sharp estimates on the logarithmic upper-tail probability $\log \Pr(X \ge E[X] +…
In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite…
Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…
In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…
We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
We study the statistics of the force felt by a particle in the class of spatially correlated distribution of identical point-like particles, interacting via a $1/r^2$ pair force (i.e. gravitational or Coulomb), and obtained by randomly…
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than expected ones, in accordance with an existing extremum…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…