Cone-constrained linear equations in Banach spaces.
Consensus of heterogeneous multi-agent systems with uncertain DoS attack: Application to mobile stage vehicles
In this paper, the consensus of heterogeneous multi-agent systems (MASs) with uncertain Deny-of-Service (DoS) attack strategies is studied. In our system, all agents are time synchronized and they communicate with each other with a constant sampling period normally. When the system is under attack, all agents use the hold-input mechanism to update the control protocol. By assuming that the attack duration is upper bounded and the occurrence of the attack follows a Markovian jumping process, the...
Constant rate distributions on partially ordered sets.
Contribution pour servir à l'étude du choix que fit A. A. Markov d'un domaine d'application de sa théorie des chaînes
Contrôle des chaînes de Markov sur des espaces arbitraires
Convergence of iterates of Lasota-Mackey-Tyrcha operators
We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.
Covariance structure of wide-sense Markov processes of order k ≥ 1
A notion of a wide-sense Markov process of order k ≥ 1, , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of is the k-dimensional process . The covariance structure of is considered in the general case and in the periodic case. In the general case it is shown that iff is a k-dimensional WM(1) process and iff the covariance function of has the triangular property....
Description de certains processus markoviens indexés par des sous-ensembles du cercle
Determinantal transition kernels for some interacting particles on the line
We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.
Discrete time markovian agents interacting through a potential
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...
Discrete time nonlinear filters with informative observations are stable.
Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs
Risk sensitive and risk neutral long run portfolio problems with consumption and proportional transaction costs are studied. Existence of solutions to suitable Bellman equations is shown. The asymptotics of the risk sensitive cost when the risk factor converges to 0 is then considered. It turns out that optimal strategies are stationary functions of the portfolio (portions of the wealth invested in assets) and of economic factors. Furthermore an optimal portfolio strategy for a risk neutral control...
Entropy of probability kernels from the backward tail boundary
A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties. On the other hand, Makarov has shown that this 'operator...
Ergodicity of a certain class of non Feller models : applications to and Markov switching models
We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.
Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models
We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.
Estimates for perturbations of general discounted Markov control chains
We extend previous results of the same authors ([11]) on the effects of perturbation in the transition probability of a Markov cost chain for discounted Markov control processes. Supposing valid, for each stationary policy, conditions of Lyapunov and Harris type, we get upper bounds for the index of perturbations, defined as the difference of the total expected discounted costs for the original Markov control process and the perturbed one. We present examples that satisfy our conditions.
Estimation and control in finite Markov decision processes with the average reward criterion
This work concerns Markov decision chains with finite state and action sets. The transition law satisfies the simultaneous Doeblin condition but is unknown to the controller, and the problem of determining an optimal adaptive policy with respect to the average reward criterion is addressed. A subset of policies is identified so that, when the system evolves under a policy in that class, the frequency estimators of the transition law are consistent on an essential set of admissible state-action pairs,...
Étude de l'estimateur du maximum de vraisemblance dans le cas d'un processus autorégressif : convergence, normalité asymptotique, vitesse de convergence
Evaluating default priors with a generalization of Eaton’s Markov chain
We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let be a class of functions on the parameter space and consider estimating elements of under quadratic loss. If the formal Bayes estimator of every function in is admissible, then the prior is strongly admissible with respect to . Eaton’s method for establishing strong admissibility is based on studying the stability properties of a particular Markov chain associated with the inferential...
Exit times of symmetric stable processes from unbounded convex domains.