Maxima and minima of stationary random sequences under a local dependence restriction.
Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model
We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [Theory Probab. Appl. 15 (1970) 1–22] and Rosiński and Żak [Stoc. Proc. Appl. 61 (1996) 277–288] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein − Uhlenbeck (supOU) processes or (fractionally integrated)...
Models of Alternating Renewal Process at Discrete Time
We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time...
Moderate deviations for stationary sequences of bounded random variables
In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of ϕ-mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.
Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
Moments of passage times for Lévy processes
Moments of some random functionals
The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.
Moving Shift Averages for Ergodic Transformations.
Moyennes et mesures en mécanique quantique et en mécanique classique
Multidimensional random processes with normal covariances