Related papers: Asymptotic Stochastic Comparison of Random Process…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…
In this paper, we consider the problem of order preservation under addition and multiplication operators over the vector space of univariate real-valued random variables. Consistent with the case of usual order over the real numbers-as…
We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…
In this manuscript, we study stochastic comparisons of the second-order statistics from dependent or independent observations with modified proportional hazard rates models. First, we establish the usual stochastic order of the second-order…
Germ order is a non-standard stochastic order defined through the comparison of the generating functions of the processes. This order was first introduced for branching random walks with a constant breeding law and independent dispersal of…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
We consider a general class of high-volume, fast-moving production-inventory systems based on both lost-sales and backorder inventory models. Such systems require a fundamental understanding of the asymptotic behavior of key performance…
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…
Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…