Weak Quenched Invariance Principle for Random Walk with Random Environment in Time
You Lü , Wenming Hong
Frontiers of Mathematics ›› 2025, Vol. 20 ›› Issue (5) : 1109 -1123.
Weak Quenched Invariance Principle for Random Walk with Random Environment in Time
Consider the invariance principle for a random walk with a random environment (denoted by μ) in time on ℝ in a weak quenched sense. We show that a sequence of random probability measures on ℝ generated by μ and a bounded Lipschitz functional f will converge in distribution to another random probability measure, which can be represented by f and two independent Brownian motions. The upper bound of the convergence rate has been obtained. We also explain that in general, this convergence can not be strengthened to the almost surely sense.
Random environment / invariance principle / weak quenched limits / 60G50
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Peking University
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