### Abstract

_{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

_{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.

Original language | English |
---|---|

Number of pages | 34 |

Journal | arXiv.org e-Print archive |

Publication status | Submitted - 2019 |

### Fingerprint

### Keywords

- Random walk
- Discrete subordination
- Bernstein function
- Parabolic Harnack inequality
- Transition probability estiamte
- Scaling condition

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Transition probability estimates for subordinate random walks.** / Cygan, Wojciech; Sebek, Stjepan.

Research output: Contribution to journal › Article › Research › peer-review

}

TY - JOUR

T1 - Transition probability estimates for subordinate random walks

AU - Cygan, Wojciech

AU - Sebek, Stjepan

PY - 2019

Y1 - 2019

N2 - Let Sn be the simple random walk on the integer lattice Zd. For a Bernstein function Φ we consider a random walk SΦn which is subordinated to Sn. Under a certain assumption on the behaviour of Φ at zero we establish global estimates for the transition probabilities of the random walk Sn. 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.

AB - Let Sn be the simple random walk on the integer lattice Zd. For a Bernstein function Φ we consider a random walk SΦn which is subordinated to Sn. Under a certain assumption on the behaviour of Φ at zero we establish global estimates for the transition probabilities of the random walk Sn. 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.

KW - Random walk

KW - Discrete subordination

KW - Bernstein function

KW - Parabolic Harnack inequality

KW - Transition probability estiamte

KW - Scaling condition

M3 - Article

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -