Transition probability estimates for subordinate random walks

2018/12/09 by Cygan, Wojciech, Šebek, Stjepan
#05C81 #35K08 #60G50 #60J10 #60J45 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.03471

Abstract

Let S_n be the simple random walk on the integer lattice ℤ^d. For a Bernstein function ϕ we consider a random walk S^ϕ_n which is subordinated to S_n. Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S^ϕ_n. The main tools that we apply are the parabolic Harnack inequality and appropriate bounds for the transition kernel of the corresponding continuous time random walk.

Related

• Harnack inequality for subordinate random walks
• Long time behaviour of random walks on the integer lattice
• One dimensional random walk killed on a finite set
• Harnack Inequalities and Local Central Limit Theorem for the Polynomial Lower Tail Random Conductance Model
• Lower bounds for bulk deviations for the simple random walk on ℤ^d, d≥ 3