Persistence probabilities for an integrated random walk bridge

Abstract

We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability $n^{-1/2}$ to stay positive. This question is motivated by so-called random polymer models and proves a conjecture by Caravenna and Deuschel.

26 pages

References in corpus (5)

• Persistence probabilities \& exponents
• On the probability that integrated random walks stay positive
• Survival probabilities of some iterated processes
• Positivity of integrated random walks
• Survival probabilities of autoregressive processes

Cited by in corpus (2)

• Persistence probabilities \& exponents
• Exit times for integrated random walks