Exit times from cones for non-homogeneous random walk with asymptotically zero drift

IM MacPhee; MV Menshikov; AR Wade

Exit times from cones for non-homogeneous random walk with asymptotically zero drift

IM MacPhee, MV Menshikov, AR Wade

School of Mathematics

Research output: Non-textual form › Web publication/site

Abstract

We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk on $\mathbb{Z}^2$ with mean drift that is asymptotically zero. Assuming bounded jumps and a form of weak isotropy, we give conditions for $\tau$ to be almost surely finite, and for the existence and non-existence of moments $\Exp [ \tau^p]$, $p>0$. Specifically, if the mean drift at $\bx \in \mathbb{Z}^2$ is of magnitude $O(\| \bx\|^{-1})$, then $\tau

Translated title of the contribution	Exit times from cones for non-homogeneous random walk with asymptotically zero drift
Original language	English
Publication status	Published - 27 Jun 2008

Access to Document

http://arxiv.org/abs/0806.4561

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title = "Exit times from cones for non-homogeneous random walk with asymptotically zero drift",

abstract = "We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk on $\mathbb{Z}^2$ with mean drift that is asymptotically zero. Assuming bounded jumps and a form of weak isotropy, we give conditions for $\tau$ to be almost surely finite, and for the existence and non-existence of moments $\Exp [ \tau^p]$, $p>0$. Specifically, if the mean drift at $\bx \in \mathbb{Z}^2$ is of magnitude $O(\| \bx\|^{-1})$, then $\tau",

author = "IM MacPhee and MV Menshikov and AR Wade",

year = "2008",

month = jun,

day = "27",

language = "English",

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TY - ADVS

T1 - Exit times from cones for non-homogeneous random walk with asymptotically zero drift

AU - MacPhee, IM

AU - Menshikov, MV

AU - Wade, AR

PY - 2008/6/27

Y1 - 2008/6/27

N2 - We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk on $\mathbb{Z}^2$ with mean drift that is asymptotically zero. Assuming bounded jumps and a form of weak isotropy, we give conditions for $\tau$ to be almost surely finite, and for the existence and non-existence of moments $\Exp [ \tau^p]$, $p>0$. Specifically, if the mean drift at $\bx \in \mathbb{Z}^2$ is of magnitude $O(\| \bx\|^{-1})$, then $\tau

AB - We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk on $\mathbb{Z}^2$ with mean drift that is asymptotically zero. Assuming bounded jumps and a form of weak isotropy, we give conditions for $\tau$ to be almost surely finite, and for the existence and non-existence of moments $\Exp [ \tau^p]$, $p>0$. Specifically, if the mean drift at $\bx \in \mathbb{Z}^2$ is of magnitude $O(\| \bx\|^{-1})$, then $\tau

M3 - Web publication/site

ER -