A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes

2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08, 90B15.

LIMIT THEOREMS FOR A GENERAL STOCHASTIC RUMOUR MODEL

We study a general stochastic rumour model in which an ignorant individual has a certain probability of becoming a stifler immediately upon hearing the rumour. We refer to this special kind of stifler as an uninterested individual. Our model also includes distinct rates for meetings between two spreaders in which both become stiflers or only one does, so that particular cases are the classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large Numbers and a Central Limit Theorem for the proportions of those who ultimately remain ignorant and those who have heard the rumour but become uninterested in it.

A Dynamic Model of Hand-and-Foot Syndrome in Patients Receiving Capecitabine

For the purpose of developing a longitudinal model to predict hand-and-foot syndrome (HFS) dynamics in patients receiving capecitabine, data from two large phase III studies were used. Of 595 patients in the capecitabine arms, 400 patients were randomly selected to build the model, and the other 195 were assigned for model validation. A score for risk of developing HFS was modeled using the proportional odds model, a sigmoidal maximum effect model driven by capecitabine accumulation as estimated through a kinetic-pharmacodynamic model and a Markov process. The lower the calculated creatinine clearance value at inclusion, the higher was the risk of HFS. Model validation was performed by visual and statistical predictive checks. The predictive dynamic model of HFS in patients receiving capecitabine allows the prediction of toxicity risk based on cumulative capecitabine dose and previous HFS grade. This dose-toxicity model will be useful in developing Bayesian individual treatment adaptations and may be of use in the clinic.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.

A note on moments of dividends

We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative L,vy risk model that was obtained in Renaud and Zhou (2007, [4]) and in Kyprianou and Palmowski (2007, [3]) and extend the result to stationary Markov processes that are skip-free upwards.

Matrix Analytic Analysis of Delays in Communication Systems

Tässä päättötyössä annetaan kuvaus kehitetystä sovelluksesta Quasi Birth Death processien ratkaisuun. Tämä ohjelma on tähän mennessä ainutlaatuinen ja sen avulla voi ratkaista sarjan tehtäviä ja sitä tarvitaan kommunikaatio systeemien analyysiin. Mainittuun sovellukseen on annettu kuvaus ja määritelmä. Lyhyt kuvaus toisesta sovelluksesta Quasi Birth Death prosessien tehtävien ratkaisuun on myös annettu

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

QoS Evaluation of BandwidthSchedulers in IPTV Networks OfferedSRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB).IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth datatransmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] First, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one incontinuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be include CAC, traffic policing used for traffic control.QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator andanalytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.

QoS evaluation of Bandwidth Schedulers in IPTV Networks Offered SRD Fluid Video Traffic

Internet protocol TV (IPTV) is predicted to be the key technology winner in the future. Efforts to accelerate the deployment of IPTV centralized model which is combined of VHO, encoders, controller, access network and Home network. Regardless of whether the network is delivering live TV, VOD, or Time-shift TV, all content and network traffic resulting from subscriber requests must traverse the entire network from the super-headend all the way to each subscriber's Set-Top Box (STB). IPTV services require very stringent QoS guarantees When IPTV traffic shares the network resources with other traffic like data and voice, how to ensure their QoS and efficiently utilize the network resources is a key and challenging issue. For QoS measured in the network-centric terms of delay jitter, packet losses and bounds on delay. The main focus of this thesis is on the optimized bandwidth allocation and smooth data transmission. The proposed traffic model for smooth delivering video service IPTV network with its QoS performance evaluation. According to Maglaris et al [5] first, analyze the coding bit rate of a single video source. Various statistical quantities are derived from bit rate data collected with a conditional replenishment inter frame coding scheme. Two correlated Markov process models (one in discrete time and one in continuous time) are shown to fit the experimental data and are used to model the input rates of several independent sources into a statistical multiplexer. Preventive control mechanism which is to be including CAC, traffic policing used for traffic control. QoS has been evaluated of common bandwidth scheduler( FIFO) by use fluid models with Markovian queuing method and analysis the result by using simulator and analytically, Which is measured the performance of the packet loss, overflow and mean waiting time among the network users.