Lecture Notes in Statistics

A. Probability and Probabilistic Methods.- Half-prophets and Robbins' problem of minimizing the expected rank.- Analysis of recursive algorithms by the contraction method.- Comparison of completely positive maps on a C*-algebra and a Lebesgue decomposition theorem.- Abel expansions and generalized Abel polynomials in stochastic models.- Positive dependence orders: a survey.- B. Markov and Other Stochastic Processes.- A Poisson limit on the number of appearances of a pattern in a Markov chain.- Palindromes in random letter generation: Poisson approximations, rates of growth and Erdos-Renyi laws.- Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains.- Explosions in Markov processes and submartingale convergence.- Probability bounds for product Poisson process.- On the first-crossing of a Poisson process on a lower boundary.- Explicit rates of convergence of stochastically ordered Markov chains.- Multi-type age-dependent branching processes with state-dependent immigration.- The nonhomogenous semi-Markov system in a stochastic environment.- Branching processes with two types of emigration and state-dependent immigration.- C. Biomathematical Models.- Remarks on the law of succession.- Large deviations of the Wright-Fisher process.- D. Epidemic Models.- Threshold behaviour in stochastic epidemics among households.- Reproduction numbers and critical immunity levels for epidemics in a community of households.- Modelling the spread of HIV in prisons.- An algorithmic study of S-I-R stochastic epidemic models.- E. Financial Models.- Testing the validity of value-at-work measures.- Option pricing for hyperbolic CRR model.- A class of shot noise models for financial applications.- Why discount? The rationale of discounting in optimization problems.- F. Random Walks and Queues.- On periodic Pollaczek waiting time processes.- Random walk approach to relaxation in disordered systems.- G. Spatial Models.- Inference for a class of causal spatial models.- Problems in the modelling and statistical analysis of earthquakes.- H. Inference.- On the existence of UMVU estimators for Bernoulli experiments in the non-identically distributed case with applications to the randomized response method and the unrelated question model.- On a three-sample test.