Some applications of the classical formula on ruin probabilities
type: Item
instance of: scholarly article
title: Some applications of the classical formula on ruin probabilities
zbMATH Open document ID: 0602.60013
DOI: 10.1016/0378-3758(86)90007-8
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: Let \(\{X_ i,i=1,2,...\}\) be a sequence of i.i.d. r.v.'s with \(P(X_ 1=+1)=P(X_ 1=-1)=1/2\). Put \(S_ 0=0\), \(S_ i=X_ 1+...+X_ i\) \((i=1,2,...)\). Starting from the well-known formula for \(P(-a<S_ j<c-a\), \(j=1,...N\), \(S_ N=k)\) (where \(a>0\), \(c>1\), \(N>0\), \(-a<k<c-a\) are integers) the author gives a rich collection of formulas for various joint distributions for unconditional and conditional random walk concerning maxima, minima and their indices. This collection and the long list of references shows, that the classical results still provide interesting new results. As an illustration, in the last section the author presents the recent results on the so-called narrowest tube problem.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 3971864
zbMATH Keywords: classical formula on ruin probabilities
zbMATH Keywords: joint distributions for unconditional and conditional random walk
zbMATH Keywords: narrowest tube problem
author: Endre Csáki
reviewed by: Antónia Földes
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90007-8
OpenAlex ID: W2077953670
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description: scientific article; zbMATH DE number 3971864