Related papers: Level crossings and other level functionals of sta…
We study the counting of level crossings for inertial random processes exposed to stochastic resetting events. We develop the general approach of stochastic resetting for inertial processes with sudden changes in the state characterized by…
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and…
In this paper, we consider smooth shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the mean number of crossings function is obtained through an integral formula.…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\tau)$. We show firstly that if $R_X(\tau)$ admits finite second and fourth derivatives at the…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension $d=1$) or hypersurface (in dimension $d\geq2$).…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
The moving average of the complex modulus of the analytic wavelet transform provides a robust time-scale representation for signals to small time shifts and deformation. In this work, we derive the Wiener chaos expansion of this…
In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…
The aim of this work is to define and perform a study of local times of all Gaussian processes that have an integral representation over a real interval (that maybe infinite). Very rich, this class of Gaussian processes, contains Volterra…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…