A limit theorem for random walks with drift
- 1 April 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (01) , 144-150
- https://doi.org/10.1017/s0021900200025304
Abstract
Let Xi , i = 1, 2, 3, … be a sequence of independent and identically distributed random variables. Write and for x ≧ 0 define M(x) + 1 is then the first passage time out of the interval (– ∞, x] for the random walk process Sn.Keywords
This publication has 10 references indexed in Scilit:
- Some Renewal Theorems with Application to a First Passage ProblemThe Annals of Mathematical Statistics, 1966
- Limiting distributions of random sums of independent random variablesProbability Theory and Related Fields, 1964
- Some inequalities for the queue GI/G/1Biometrika, 1962
- The maximum of sums of stable random variablesTransactions of the American Mathematical Society, 1956
- A combinatorial lemma and its application to probability theoryTransactions of the American Mathematical Society, 1956
- On the oscillation of sums of random variablesTransactions of the American Mathematical Society, 1952
- Asymptotic distribution of the maximum cumulative sum of independent random variablesBulletin of the American Mathematical Society, 1948
- Limit distribution of the maximum and minimum of successive cumulative sums of random variablesBulletin of the American Mathematical Society, 1947
- On certain limit theorems of the theory of probabilityBulletin of the American Mathematical Society, 1946
- The fundamental limit theorems in probabilityBulletin of the American Mathematical Society, 1945