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In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…
In this paper, we establish the existence of moments and moment estimates for L\'evy-type processes. We discuss whether the existence of moments is a time dependent distributional property, give sufficient conditions for the existence of…
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
Cascades of Poisson processes are probabilistic models for spatio-temporal phenomena in which (i) previous events may trigger subsequent events, and (ii) both the background and triggering processes are conditionally Poisson. Such phenomena…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
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…
A version of scattering theory that was developed many years ago to treat nuclear scattering processes, has provided a powerful tool to study universality in scattering processes involving open quantum systems with underlying classically…
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap,…
We explore the finite dimensional distributions of the second-order scattering transform of a class of non-Gaussian processes when all the scaling parameters go to infinity simultaneously. For frequently used wavelets, we find a coupling…
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…