Related papers: Quasi-continuous random variables and processes un…
We suggest to investigate certain non-standard (pseudo-)differential operators in order to construct and to study multi-parameter processes. Our approach will include "classical" multi-parameter Markov processes but will go eventually far…
The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to…
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…
Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…
A new method of quasi-optimal observables allows one to approach the quality of data processing usually associated with the method of maximal likelihood within the simpler algorithmic context of generalized moments.
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
A well-known It\^o formula for finite dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the…
Efficient and effective modeling of complex systems, incorporating cloud physics and precipitation, is essential for accurate climate modeling and forecasting. However, simulating these systems is computationally demanding since…
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a…
Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…
In this paper we develop the theory of {\it polymorphisms} of measure spaces, which is a generalization of the theory of measure-preserving transformations; we describe the main notions and discuss relations to the theory of Markov…
We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we…
We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aperiodic absorbed Markov chains, we obtain exponential…