Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

Probabilistic models to assist maintenance of multiple instruments

The paper discusses maintenance challenges of organisations with a huge number of devices and proposes the use of probabilistic models to assist monitoring and maintenance planning. The proposal assumes connectivity of instruments to report relevant features for monitoring. Also, the existence of enough historical registers with diagnosed breakdowns is required to make probabilistic models reliable and useful for predictive maintenance strategies based on them. Regular Markov models based on estimated failure and repair rates are proposed to calculate the availability of the instruments and Dynamic Bayesian Networks are proposed to model cause-effect relationships to trigger predictive maintenance services based on the influence between observed features and previously documented diagnostics

Modelo discreto de transiciones entre estados de dependencia

En este trabajo se analiza el modelo markoviano de transiciones anuales entre estados de dependencia asumiendo la hipótesis de estacionariedad. Se suponen conocidas las tasas de mortalidad de la población autónoma y las tasas de prevalencia de los tres estados de dependencia considerados. La indeterminación del modelo se resolverá incorporando restricciones en forma de hipótesis en las interrelaciones, a partir de las cuales se obtienen las matrices de transición por edades y se analiza el comportamiento de las mismas. Se realizan aplicaciones numéricas utilizando distribuciones de mortalidad y de prevalencia que pueden ser adecuadas para la población española y que han surgido de un análisis preliminar. Por último, se efectúa un análisis de sensibilidad de los resultados respecto al cambio de hipótesis en las mencionadas interrelaciones. Abstract

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

Selecting negotiation processes with Health Care

We address the question of how a third-party payer (e.g. an insurer) decides what providers to contract with. Three different mechanisms are studied and their properties compared. A first mechanism consists in the third-party payer setting up a bargaining procedure with both providers jointly and simultaneously. A second mechanism envisages the outcome of the same simultaneous bargaining but independently with every provider. Finally, the last mechanism is of different nature. It is the so-called "any willing provider" where the third-party payer announces a contract and every provider freely decides to sign it or not. The main finding is that the decision of the third-party payer depends on the surplus to be shared. When it is relatively high the third-party payer prefers the any willing provider system. When, on the contrary, the surplus is relatively low, the third-party payer will select one of the other two systems accor ing to how bargaining power is distributed.

Dance movement patterns recognition

"Es tracta d'un projecte dividit en dues parts independents però complementàries, realitzades per autors diferents. Aquest document conté originàriament altre material i/o programari només consultable a la Biblioteca de Ciència i Tecnologia"

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks.