The Annals of Probability

On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive

Erwin Bolthausen

Full-text: Open access

Abstract

Let $\{X_k: k \geqq 1\}$ be a sequence of i.i.d.rv with $E(X_i) = 0$ and $E(X_i^2) = \sigma^2, 0 < \sigma^2 < \infty$. Set $S_n = X_1 + \cdots + X_n$. Let $Y_n(t)$ be $S_k/\sigma n^\frac{1}{2}$ for $t = k/n$ and suitably interpolated elsewhere. This paper gives a generalization of a theorem of Iglehart which states weak convergence of $Y_n(t)$, conditioned to stay positive, to a suitable limiting process.

Article information

Source
Ann. Probab. Volume 4, Number 3 (1976), 480-485.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996098

Digital Object Identifier
doi:10.1214/aop/1176996098

Mathematical Reviews number (MathSciNet)
MR415702

Zentralblatt MATH identifier
0336.60024

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J15

Keywords
Conditioned limit theorem functional central limit theorem random walks weak convergence

Citation

Bolthausen, Erwin. On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive. Ann. Probab. 4 (1976), no. 3, 480--485. doi:10.1214/aop/1176996098. https://projecteuclid.org/euclid.aop/1176996098


Export citation