Jan Grandell – författare

Sannolikhetsteori och statistikteori har vidsträckta tillämpningar inom olika forskningsområden och olika delar av samhällslivet. Bland annat naturvetare och tekniker har god nytta av kunskaper om dessa teorier och deras användning.Denna bok, som är en omarbetning av en tidigare bok av Gunnar Blom, behandlar de grundläggande delarna av sannolikhetsteorinoch statistikteorin. De många lösta exemplen i texten underlättar läsningen. Övningsproblem med svar avslutar flertalet kapitel.Boken är avsedd för kurser av olika slag men är också lämplig för självstudier.Från och med sjunde upplagan ges denna bok åter ut som hårdband. Denna upplaga innehåller dock inga förändringar av innehållet jämfört med femte och sjätte upplagan.

About fifteen years ago Henning Rodhe and I disscussed the calculation of residence times, or lifetimes, of certain air pollutants for the first time. He was interested in pollutants which were mainly removed from the atmosphere by precipitation scavenging. His idea was to base the calculation on statistical models for the variation of the precipitation i~tensity and not only on the average precipitation intensity. In order to illustrate the importance of taking the variation into account we considered a simple model - here called the Markov model - for the precipitation intensity and computed the distribution of the residence time of an aerosol particle. Our expression for the average residence time - here formula (13- was rather much used by meteorologists. Certainly we were pleased, but while our ambition had been to provide an illustration, our work was merely understood as a proposal for a realistic model. Therefore we found it natural to search for more general models. The mathematical problems involved were the origin of my interest in this field. A brief outline of the background, purpose and content of this paper is given in section 1. It is a pleasure to thank Gunnar Englund, Georg Lindgren, Henning Rodhe and Michael Stein for their substantial help in the pre­ paration of this paper and Iren Patricius for her assistance in typing.

About fifteen years ago Henning Rodhe and I disscussed the calculation of residence times, or lifetimes, of certain air pollutants for the first time. He was interested in pollutants which were mainly removed from the atmosphere by precipitation scavenging. His idea was to base the calculation on statistical models for the variation of the precipitation i~tensity and not only on the average precipitation intensity. In order to illustrate the importance of taking the variation into account we considered a simple model - here called the Markov model - for the precipitation intensity and computed the distribution of the residence time of an aerosol particle. Our expression for the average residence time - here formula (13- was rather much used by meteorologists. Certainly we were pleased, but while our ambition had been to provide an illustration, our work was merely understood as a proposal for a realistic model. Therefore we found it natural to search for more general models. The mathematical problems involved were the origin of my interest in this field. A brief outline of the background, purpose and content of this paper is given in section 1. It is a pleasure to thank Gunnar Englund, Georg Lindgren, Henning Rodhe and Michael Stein for their substantial help in the pre­ paration of this paper and Iren Patricius for her assistance in typing.

Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.