Related papers: Measure-Valued Generators of General Piecewise Det…
Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found…
Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control…
Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs…
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For…
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant…
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or…
We consider a Markovian evolution on point processes, the $\Psi$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a…
Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…
Variance reduction methods are often needed for the reliability assessment of complex industrial systems, we focus on one variance reduction method in a given context, that is the interacting particle system method (IPS) used on piecewise…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
General Markov chains in an arbitrary phase space are considered in the framework of the operator treatment. Markov operators continue from the space of countably additive measures to the space of finitely additive measures. Cycles of…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
This paper introduces Switching Processes, called SP. Their constructions are inspired by the PDMP's ones (PDMP stands for Piecewise Deterministic Markov Process). A Markov process, called the intrinsic process, replaces the PDMP's flow.…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
We extend Monte Carlo samplers based on piecewise deterministic Markov processes (PDMP samplers) by formally defining different boundary conditions such as sticky floors, soft and hard walls and teleportation portals. This allows PDMP…
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the…
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product…
We consider a type of Markov property for set-indexed processes which is satisfied by all processes with independent increments and which allows us to introduce a transition system theory leading to the construction of the process. A…
We propose deterministic timed automata (DTA) as a model-independent language for specifying performance and dependability measures over continuous-time stochastic processes. Technically, these measures are defined as limit frequencies of…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…