scholarly journals Journals Cited in Ann. Math. Statist. , Vols. 1-31 (1930-1960)

1962 ◽  
Vol 0 (0) ◽  
pp. 629-644
Keyword(s):  
1946 ◽  
Vol 6 (02) ◽  
pp. 77-82

There is a high chance against your picking up any recent number of theBulletin de l'Association des Actuaires suisseswhich does not contain an article dealing with the theory of the changing population ‘Le renouvellement, quelques problèmes connexes et les équations intégrates du cycle fermé (Féraud, vol. XLI, 1941, p. 81) and ‘Über die Integralgleichung der Bevölkerungstheorie’ (Hadwiger, vol. XXXVIII, 1939, p. I) are two titles of papers belonging to this category. The English names for the relevant notions can be found in many publications by Lotka (e.g. ‘The theory of industrial replacement’, Skand,Aktuar Tidskr.1940; ‘On an integral equation in population analysis’, Ann. math. Statist. 1939; ‘The structure of a growing population’,Human Biology, vol. III) and one can nearly always see that a paper deals with this subject by noticing an equation of the following form:from which the function G (t) is to be determined. (For a purely mathematical investigation of this ‘integral equation of the second type’ see Feller, ‘On the integral equation of renewal theory’,Ann. math. Statist.Vol. XII, 1941, and compare also C. D. Rich,J.I.A.Vol. LXV).


2020 ◽  
Vol 26 (2) ◽  
pp. 309-314
Author(s):  
Zhenxia Liu ◽  
Yurong Zhu

AbstractWe continue our investigation on general large deviation principles (LDPs) for longest runs. Previously, a general LDP for the longest success run in a sequence of independent Bernoulli trails was derived in [Z. Liu and X. Yang, A general large deviation principle for longest runs, Statist. Probab. Lett. 110 2016, 128–132]. In the present note, we establish a general LDP for the longest success run in a two-state (success or failure) Markov chain which recovers the previous result in the aforementioned paper. The main new ingredient is to implement suitable estimates of the distribution function of the longest success run recently established in [Z. Liu and X. Yang, On the longest runs in Markov chains, Probab. Math. Statist. 38 2018, 2, 407–428].


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