This paper presents a new lower bound for the recursive algorithm for solving parity games which is induced by the constructive proof of memoryless determinacy by Zielonka. We outline a family of games of linear size on which the algorithm requires exponential time.

In this paper we consider stochastic recursive equations of sum type, , and of max type, , where Ai, bi, and b are random, (Xi) are independent, identically distributed copies of X, and denotes equality in distribution. Equations of these types typically characterize limits in the probabilistic analysis of algorithms, in combinatorial optimization problems, and in many other problems having a recursive structure. We develop some new contraction properties of minimal Ls-metrics which allow us to establish general existence and uniqueness results for solutions without imposing any moment conditions. As an application we obtain a one-to-one relationship between the set of solutions to the homogeneous equation and the set of solutions to the inhomogeneous equation, for sum- and max-type equations. We also give a stochastic interpretation of a recent transfer principle of Rösler from nonnegative solutions of sum type to those of max type, by means of random scaled Weibull distributions.

In this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case.

We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature.

This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution.

This paper presents a new recursive algorithm of robot dynamics based on the Kane's dynamic equations and Newton-Euler formulations. Differing from Kane's work, the algorithm is general-purpose and can be easily realized on computers. It is suited not only for robots with all rotary joints but also for robots with some prismatic joints. Formulations of the algorithm keep the recurrence characteristics of the Newton-Euler formulations, but possess stronger physical significance. Unlike the conventional algorithms, such as the Lagrange and Newton-Euler algorithm, etc., the algorithm can be used to deal with dynamics of robots containing closed chains without cutting the closed chains open. In addition, this paper makes a comparison between the algorithm and those conventional algorithms from the number of multiplications and additions.

Based on a representation of the aggregate claims random variable as linear combination of counting random variables, a linear multivariate Bayesian model of risk theory is defined. In case of the classical risk theoretical assumptions, that is conditional Poisson likelihood counting variates and Gamma structural density, the model is shown to identify with a Bayesian version of the collective model of risk theory. An interesting multivariate credibility formula for the predictive mean is derived. A new type of recursive algorithm, called three-stage nested recursive scheme, allows to evaluate the predictive density and associated predictive stop-loss premiums in an effective way.