Random walks in time-inhomogeneous random environment conditioned to stay positive

2022/11/28 by Wenming Hong, Hong, Wenming, Shengli Liang +1
Computer Science · Mathematics · #60F17 #60G50 #60K37 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2211.15017

openalex publication_date 2022/11/28 · openalex created_date 2022/12/10 · openalex updated_date 2026/07/28

Abstract

We consider a random walk \S_n\_{n∈ ℕ} in time-inhomogeneous random environment ξ. For almost each realization of ξ, we formulate a quenched harmonic function, based on which we can define the random walk in random environment conditioned to stay positive by the Doob's h-transform. Furthermore, we prove a quenched invariance principle for the conditioned random walk for almost each realization of ξ.

Related

• Quenched invariance principle for random walk in time-dependent balanced\n random environment
• Weak Quenched Invariance Principle for Random Walk with Random Environment in Time
• Almost Sure Invariance Principle for Continuous-Space Random Walk in Dynamic Random Environment
• Quenched invariance principle for long range random walks in balanced random environments
• Multidimensional random walks conditioned to stay ordered via generalized ladder height functions