132 research outputs found
Numerical method for impulse control of Piecewise Deterministic Markov Processes
This paper presents a numerical method to calculate the value function for a
general discounted impulse control problem for piecewise deterministic Markov
processes. Our approach is based on a quantization technique for the underlying
Markov chain defined by the post jump location and inter-arrival time.
Convergence results are obtained and more importantly we are able to give a
convergence rate of the algorithm. The paper is illustrated by a numerical
example.Comment: This work was supported by ARPEGE program of the French National
Agency of Research (ANR), project "FAUTOCOES", number ANR-09-SEGI-00
Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems
The aim of this paper is to propose a new numerical approximation of the
Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is
based on the selection of typical trajectories of the driving semi-Markov chain
of the process by using an optimal quantization technique. The main advantage
of this approach is that it makes pre-computations possible. We derive a
Lipschitz property for the solution of the Riccati equation and a general
result on the convergence of perturbed solutions of semi-Markov switching
Riccati equations when the perturbation comes from the driving semi-Markov
chain. Based on these results, we prove the convergence of our approximation
scheme in a general infinite countable state space framework and derive an
error bound in terms of the quantization error and time discretization step. We
employ the proposed filter in a magnetic levitation example with markovian
failures and compare its performance with both the Kalman-Bucy filter and the
Markovian linear minimum mean squares estimator
Numerical method for expectations of piecewise-determistic Markov processes
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
quantization of an underlying discrete-time Markov chain. We obtain bounds for
the rate of convergence of the algorithm. The approximation we propose is
easily computable and is flexible with respect to some of the parameters
defining the problem. Two examples illustrate the paper.Comment: 41 page
Random coefficients bifurcating autoregressive processes
This paper presents a model of asymmetric bifurcating autoregressive process
with random coefficients. We couple this model with a Galton Watson tree to
take into account possibly missing observations. We propose least-squares
estimators for the various parameters of the model and prove their consistency
with a convergence rate, and their asymptotic normality. We use both the
bifurcating Markov chain and martingale approaches and derive new important
general results in both these frameworks
Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data
We present symmetry tests for bifurcating autoregressive processes (BAR) when
some data are missing. BAR processes typically model cell division data. Each
cell can be of one of two types \emph{odd} or \emph{even}. The goal of this
paper is to study the possible asymmetry between odd and even cells in a single
observed lineage. We first derive asymmetry tests for the lineage itself,
modeled by a two-type Galton-Watson process, and then derive tests for the
observed BAR process. We present applications on both simulated and real data
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