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We introduce a class of spatial stochastic processes in the max-domain of attraction of familiar max-stable processes. The new class is based on Cox processes and comprises models with short range dependence. We show that statistical…
Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
The paper studies thin times which are random times whose graph is contained in a countable union of the graphs of stopping times with respect to a reference filtration $\mathbb F$. We show that a generic random time can be decomposed into…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
We generalize the method of Van Hove so as to deal with the case of non-ordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of…
The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…
Modeling a precipitation field is challenging due to its intermittent and highly scale-dependent nature. Motivated by the features of high-frequency precipitation data from a network of rain gauges, we propose a threshold space-time $t$…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Invariance times are stopping times $\tau$ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $\tau$ , are local martingales with respect to the original model…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…