Optimal stopping of a sequence of maxima between random and fixed barriers
Optimal stopping of a sequence of maxima over an unobservable sequence of maxima
Optimum stopping rules on the sequence of statistically dependent vectors
Order Dentability and the Radon-Nikodym Property in Banach Lattices.
Parada óptima con horizonte aleatorio.
Analizamos el problema de parada óptima con horizonte aleatorio en procesos de Markov con tiempo continuo. En concreto, estudiamos el caso en el que el horizonte es el tiempo de primera entrada en el interior de un cerrado B. Definimos las funciones B-excesivas y vemos su relación con el pago del problema de parada óptima. Posteriormente introducimos varios conjuntos, que aparecen de forma natural en el problema y que nos permiten caracterizar los dominios de parada. Por último consideramos el caso...
Parametrization and geometric analysis of coordination controllers for multi-agent systems
In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.
Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal
Problèmes à frontière libre et arbres de mesures
Problèmes de temps d'arrêt optimal pour les systèmes distribués stochastiques
Processus de Ray et théorie du balayage.
Prophet Inequalities for Averages of Independent Non-Negative Random Variables.
Quantized distributed output regulation of multi-agent systems
Motivated by digital communication channel, we consider the distributed output regulation problem for linear multi-agent systems with quantized state measurements. Quantizers take finitely many values and have an adjustable "zoom" parameter. Quantized distributed output regulation concerns designing distributed feedback by employing quantized technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. With the solvability conditions...
Quantum stopping times and quasi-left continuity
Quelques inégalités concernant les martingales
Quelques résultats sur les maisons de jeu analytiques
Random hysteresis loops
Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order , the size of the system, the “critical” hysteresis loop becomes random.
Random priority two-person full-information best choice problem with imperfect observation
The following version of the two-player best choice problem is considered. Two players observe a sequence of i.i.d. random variables with a known continuous distribution. The random variables cannot be perfectly observed. Each time a random variable is sampled, the sampler is only informed whether it is greater than or less than some level specified by him. The aim of the players is to choose the best observation in the sequence (the maximal one). Each player can accept at most one realization of...
Random walks in with non-zero drift absorbed at the axes
Spatially homogeneous random walks in with non-zero jump probabilities at distance at most , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.
Reflected backward stochastic differential equations with two RCLL barriers
In this paper we consider BSDEs with Lipschitz coefficient reflected on two discontinuous (RCLL) barriers. In this case, we prove first the existence and uniqueness of the solution, then we also prove the convergence of the solutions of the penalized equations to the solution of the RBSDE. Since the method used in the case of continuous barriers (see Cvitanic and Karatzas, Ann. Probab.24 (1996) 2024–2056 and Lepeltier and San Martín, J. Appl. Probab.41 (2004) 162–175) does not work, we develop...
Refracted Lévy processes
Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation dUt=−δ1{Ut>b} dt+dXt, where X={Xt : t≥0} is a Lévy...