## The Annals of Probability

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

Erwin Bolthausen

#### 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

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