engleski

Transition probability estimates for subordinate random walks

Let S_n be the simple random walk on the integer lattice Z^d. For a Bernstein function fwe consider a random walk S^f_n which is subordinated to S_n. Under a certain assumption on the behaviour of fat zero we establish global estimates for the transition probabilities of the random walk S^f_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.

random walk ; discrete subordination ; Bernstein function ; parabolic Harnack inequality ; transition probability estimate ; scaling condition

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