Survival time of a heterogeneous random walk in a quadrant

Boundary behavior for random walks in cones

“…with τ x defined in (3). Remark that the above identity for n = 1 implies all the other relations for n 2.…”

“…Likewise, by [15, Eq. ( 76)], there exist constants a, C such that for all y ∈ K (3) and z ∈ K 1 (y),…”

“…Ben-Salem, Mustapha and Sifi [3] obtain upper Gaussian estimates of transition probabilities of some models of space-inhomogeneous random walks on the positive quadrant. These bounds have a form comparable to (5).…”

Upper estimates for inhomogeneous random walks confined to the positive orthant

“…Regarding spatially non-homogeneous walks, only few results are available; see [31] for half-space non-homogeneous walks and [2,7,10,24] for quadrant walks. By spatially non-homogeneous walk on Z d , we mean a discrete-time-homogenous Markov chain on Z d which is spatially non-homogeneous, see [29].…”

“…The main purpose of this paper is to establish upper Gaussian estimates for the transition kernels of a large class of spatially non-homogeneous random walks killed on the boundary of the orthant O d + . We refine the approach used in the case of the half-space Z d + [31] and in the case of models with one dimensional space inhomogeneity on the positive quadrant [2].…”