Related papers: Observables of Macdonald processes
The main objective of the present article is to characterize regular Fredholm pairs and chains in terms of Fredholm operators.
To find moments of various estimators related to Autoregressive models of Statistics, one first needs the cumulants of products of two Normally distributed random variables. The purpose of this article is to derive the corresponding…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
In this work it is introduced the notion of regular Fredholm pair, i.e. a Fredholm pair whose operators are regular. The main properties of these objects are studied, and what is more, they are entirely classified. Furthermore, the index of…
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider a class of generalized coarsened procedures for confounding. At a…
The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fd\omega$ relies on independent samples from $\omega$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive…
We obtain a formula for the $n$-dimensional distributions of the Airy$_1$ process in terms of a Fredholm determinant on $L^2(\rr)$, as opposed to the standard formula which involves extended kernels, on $L^2(\{1,...,n\}\times\rr)$. The…
We obtain asymptotics for the Airy kernel Fredholm determinant on two intervals. We give explicit formulas for all the terms up to and including the oscillations of order $1$, which are expressed in terms of Jacobi $\theta$-functions.
In this expository article we describe the asymptotics of certain Fredholm determinants which provide solutions to the cylindrical Toda equations, and we explain how these asymptotics are derived. The connection with Fredholm determinants…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.
We present explicit formulas for the Macdonald polynomials of types $C_n$ and $D_n$ in the one-row case. In view of the combinatorial structure, we call them "tableau formulas". For the construction of the tableau formulas, we apply some…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
We consider method-of-quantiles estimators of unknown parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level lambda in (0,1). The aim is to present…
In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…
In this paper the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite-activity subordinators induced by the probability distribution of the running…