Local probabilities for random walks conditioned to stay positive

Let S 0  = 0, { S n ,  n  ≥ 1} be a random walk generated by a sequence of i.i.d. random variables X 1 , X 2 , . . . and let and . Assuming that the distribution of X 1 belongs to the domain of attraction of an α -stable law we study the asymptotic behavior, as , of the local probabilities and prove...

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Bibliographic Details
Published inProbability theory and related fields Vol. 143; no. 1-2; pp. 177 - 217
Main Authors Vatutin, Vladimir A., Wachtel, Vitali
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.01.2009
Springer Nature B.V
Subjects
Asymptotic properties
Economics
Finance
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Random walk
Statistics for Business
Theorems
Theoretical
Stable laws
Limit theorems
Random walks
60G52
60E07
60G50
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Summary:Let S 0  = 0, { S n ,  n  ≥ 1} be a random walk generated by a sequence of i.i.d. random variables X 1 , X 2 , . . . and let and . Assuming that the distribution of X 1 belongs to the domain of attraction of an α -stable law we study the asymptotic behavior, as , of the local probabilities and prove the Gnedenko and Stone type conditional local limit theorems for the probabilities with fixed Δ and .
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-007-0124-8