In this paper, we develop simple models to study the performance of BitTorrent, a second generation peerto -peer (P2P) application. We first present a simple fluid model and study the scalability, performance and e#ciency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its e#ect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet.

This paper presents a dynamic asset-pricing model under asymmetric information. Investors have different information concerning the future growth rate of dividends. They rationally extract information from prices as well as dividends and maximize their expected utility. The model has a closed-form solution to the rational expectations equilibrium. We find that existence of uninformed investors increases the risk premium. Supply shocks can affect the risk premium only under asymmetric information. Information asymmetry among investors can increase price volatility and negative autocorrelation in returns. Less-informed investors may rztionally behave like price chasers.

The analysis of uni- or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory.

Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al.[2], Ji & Chizeck [6] and Marlton [13]. The aim of this paper is to discuss the exponential stability for general nonlinear stochastic differential equations with Markovian switching.

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given

Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.

Abstract — We develop a model for General Stochastic Hybrid Systems (GSHS) which is a generalization of Piecewise-Deterministic Markov Processes (PDMP), introduced by Davis and stochastic hybrid systems proposed by Hu, Lygeros and Sastry. This model possesses certain desirable properties, as the strong Markov property and the càdlàg property. Extending results available for PDMP, we develop the extended generator formula and the differential formula for GSHS. Then we investigate the dynamic programming for GSHS, using the differential formula. I.

Abstract. In this paper we generalize a model for stochastic hybrid systems. First, we prove that this model is a right Markov process and it satisfies some mathematical properties. Second, we propose a method based on the theory of Dirichlet forms to study the reachability problem associated with these systems.

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Abstract: An overview of Stochastic Hybrid Models developed in the literature is presented. Attention is concentrated on three classes of models: Piecewise Deterministic Markov Processes, Switching Diffusion Processes and Stochastic Hybrid Systems. The descriptive power of the three classes is compared and conditions under which the classes coincide are developed. The theoretical analysis is motivated by modelling problems in Air Traffic Management. Copyright, 2003, IFAC