With Andrzej Lasota There and Back Again
Annales Mathematicae SilesianaeThe paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota’s results on the author’s research concerning various fields of ...
Rudnicki Ryszard
doaj +1 more source
Analysis Of Upwind Method For Piecewise Deterministic Markov Processes [PDF]
Computational Methods in Applied Mathematics, 2008 AbstractA numerical upscaling approach, NU, for solving multiscale elliptic problems is discussed. The main components of this NU are: i) local solve of aux-iliary problems in grid blocks and formal upscaling of the obtained results to build a coarse scale equation; ii) global solve of the upscaled coarse scale equation; and iii) reconstruction of a ...
openaire +3 more sources
Robust estimation for Markov chains with applications to Piecewise-deterministic Markov Processes,
, 2018 International audiencePiecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated
Tillier, Charles +2 more
core
Numerical methods for the exit time of a piecewise-deterministic Markov process
, 2012 International audienceWe present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP).
de Saporta, Benoîte +2 more
core +1 more source
Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach [PDF]
, 2006 We propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model.
Davy, Manuel +2 more
core +1 more source
DESIGN-ADAPTIVE POINTWISE NONPARAMETRIC REGRESSION ESTIMATION FOR RECURRENT MARKOV TIME SERIES [PDF]
A general framework is proposed for (auto)regression nonparametric estimation of recurrent time series in a class of Hilbert Markov processes with a Lipschitz conditional mean.
Guerre
core
Numerical methods for piecewise deterministic Markov processes with boundary
, 2017 We study the approximation of the distribution of Piecewise Deterministic Markov Processes jumping when the process reaches some boundary of the domain. We first introduce an equation to which the marginal distributions of the process are solution, which
Eymard, Robert +3 more
core +1 more source
Variability and singularity arising from a Piecewise-Deterministic Markov Process applied to model poor patient compliance in the multi-IV case. [PDF]
J Appl Stat, 2020 Fermín LJ, Lévy-Véhel J.
europepmc +1 more source
, 2007 International audienceWe study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (
Limnios, Nikolaos, Chiquet, Julien
core +1 more source
Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes * [PDF]
, 2012 International audienceA classical random walk (S t , t ∈ N) is defined by S t := t n=0 X n , where (X n) are i.i.d. When the increments (X n) n∈N are a one-order Markov chain, a short memory is introduced in the dynamics of (S t).
Pierre Vallois +8 more
core