494 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
Tail of a linear diffusion with Markov switching
Let Y be an Ornstein-Uhlenbeck diffusion governed by a stationary and ergodic
Markov jump process X: dY_t=a(X_t)Y_t dt+\sigma(X_t) dW_t, Y_0=y_0. Ergodicity
conditions for Y have been obtained. Here we investigate the tail propriety of
the stationary distribution of this model. A characterization of either heavy
or light tail case is established. The method is based on a renewal theorem for
systems of equations with distributions on R.Comment: Published at http://dx.doi.org/10.1214/105051604000000828 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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
Optimal stopping for partially observed piecewise-deterministic Markov processes
This paper deals with the optimal stopping problem under partial observation
for piecewise-deterministic Markov processes. We first obtain a recursive
formulation of the optimal filter process and derive the dynamic programming
equation of the partially observed optimal stopping problem. Then, we propose a
numerical method, based on the quantization of the discrete-time filter process
and the inter-jump times, to approximate the value function and to compute an
actual -optimal stopping time. We prove the convergence of the
algorithms and bound the rates of convergence
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
Predictive maintenance for the heated hold-up tank
We present a numerical method to compute an optimal maintenance date for the
test case of the heated hold-up tank. The system consists of a tank containing
a fluid whose level is controlled by three components: two inlet pumps and one
outlet valve. A thermal power source heats up the fluid. The failure rates of
the components depends on the temperature, the position of the three components
monitors the liquid level in the tank and the liquid level determines the
temperature. Therefore, this system can be modeled by a hybrid process where
the discrete (components) and continuous (level, temperature) parts interact in
a closed loop. We model the system by a piecewise deterministic Markov process,
propose and implement a numerical method to compute the optimal maintenance
date to repair the components before the total failure of the system.Comment: arXiv admin note: text overlap with arXiv:1101.174
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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