TY - JOUR
TI - From Pseudorandom Walk to Pseudo-Brownian Motion: First Exit Time from a One-Sided or a Two-Sided Interval
VL - 2014
PY - 2014
DA - 2014/03/26
DO - 10.1155/2014/520136
UR - https://doi.org/10.1155/2014/520136
AB - Let be a positive integer, a positive constant and be a sequence of independent identically distributed pseudorandom variables. We assume that the ’s take their values in the discrete set and that their common pseudodistribution is characterized by the (positive or negative) real numbers for any . Let us finally introduce the associated pseudorandom walk defined on by and for . In this paper, we exhibit some properties of . In particular, we explicitly determine the pseudodistribution of the first overshooting time of a given threshold for as well as that of the first exit time from a bounded interval. Next, with an appropriate normalization, we pass from the pseudorandom walk to the pseudo-Brownian motion driven by the high-order heat-type equation . We retrieve the corresponding pseudodistribution of the first overshooting time of a threshold for the pseudo-Brownian motion (Lachal, 2007). In the same way, we get the pseudodistribution of the first exit time from a bounded interval for the pseudo-Brownian motion which is a new result for this pseudoprocess.
JF - International Journal of Stochastic Analysis
SN - 2090-3332
PB - Hindawi Publishing Corporation
SP - 520136
KW -
A2 - Lopez-Herrero, M.
AU - Lachal, Aimé
ER -