Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific engineering disciplines. Two key frameworks that have emerged for modeling solving control problems stochastic are piecewise deterministic Markov processes (PDMPs) decision (MDPs). Each framework has its unique strengths, their intersection offers promising opportunities tackling broad class problems, particularly context impulse controls decision-making...

We study the asymptotic behavior of least squares estimators unknown parameters general pth-order bifurcating autoregressive processes. Under very weak assumptions on driven noise process, namely conditional pair-wise independence and suitable moment conditions, we establish almost sure convergence our together with quadratic strong law central limit theorem. All analysis relies non-standard results for martingales.

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article 1984. Today it is used to model a variety complex systems fields engineering, economics, management sciences, biology, Internet traffic, networks and many more. Yet, despite this, there very little way literature devoted development numerical methods for PDMDs solve problems practical importance, or computational control PDMPs. This book therefore presents collection...

We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some data are missing. In this aim, we model observed by a two-type Galton-Watson consistent with binary tree structure data. Under independence between leading to missing and BAR suitable assumptions on driven noise, establish strong consistency our estimators set non-extinction Galton-Watson, via martingale approach. also prove quadratic law asymptotic normality.

The aim of this paper is to propose a new numerical approximation the Kalman-Bucy filter for semi-Markov jump linear systems. This based on selection typical trajectories driving chain process by using an optimal quantization technique. main advantage approach that it makes pre-computations possible. We derive Lipschitz property solution Riccati equation and general result convergence perturbed solutions switching equations when perturbation comes from chain. Based these results, we prove...

We propose a numerical method to approximate the value function for optimal stopping problem of piecewise deterministic Markov process (PDMP).Our approach is based on quantization post jump locationinter-arrival time chain naturally embedded in PDMP, and pathadapted discretization grids.It allows us derive bounds convergence rate algorithm provide computable -optimal time.The paper illustrated by example.

This paper presents a numerical method to compute the optimal maintenance time for complex dynamic system applied an example of metallic structure subject corrosion. An arbitrarily early intervention may be uselessly costly, but late one lead partial/complete failure system, which has avoided. One must therefore find balance between these too-simple policies. To achieve this aim, is modelled by stochastic hybrid process. The problem thus corresponds stopping problem. A proposed solve and...

We present a numerical method to compute the survival function and moments of exit time for piecewise-deterministic Markov process (PDMP). Our approach is based on quantization an underlying discrete-time chain related PDMP. The approximation we propose easily computable even flexible with respect consider. prove convergence algorithm obtain bounds rate in case moments. give academic example model from reliability field illustrate results paper.

This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this Galton−Watson tree to take into account possibly missing observations. propose least-squares estimators for the various parameters and prove their consistency, convergence rate, asymptotic normality. use both Markov chain martingale approaches derive results in these frameworks.

We present a numerical method to compute expectations of functionals piecewise deterministic Markov process.We discuss time dependent as well horizon problems.Our approach is based on the quantization an underlying discrete-time chain.We obtain bounds for rate convergence algorithm.The approximation we propose easily computable and flexible with respect some parameters defining problem.An example illustrates paper.1. Introduction 63 2. Definitions assumptions 67 3. Expectation 71 4....

This paper <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> describes an original approach based on dynamic programming theory (discrete-time finite horizon Markov control) to address the difficult problem of computing optimal trajectories with respect some criteria for any vehicle evolving in a given environment (in probabilistic point view) accomplish tasks (defined complex Lipschitz criteria). After brief remind about The whole control...

This paper studies optimal mean square error estimation for discrete-time linear systems with observed Markov jump parameters. New estimators are introduced by considering a cluster information structure in the filter design. The set of filters constructed this way can be ordered lattice according to refines clusters chain, including Markovian estimator at one end (with only cluster) and Kalman other as many states). higher is number clusters, heavier precomputations smaller embedded...

The data we analyze derives from the observation of numerous cells bacterium Escherichia coli (E. coli) growing and dividing. Single grow divide to give birth two daughter cells, that in turn divide. Thus, a colony single ancestor is structured as binary genealogical tree. At each node measured growth rate bacterium. In this paper, study different sets. One set corresponds small complete trees, whereas other one long specific sub-trees. Our aim compare both This paper accessible post...