TY - JOUR
T1 - Lower Deviation for the Supremum of the Support of Super-Brownian Motion
AU - Ren, Yan Xia
AU - Song, Renming
AU - Zhang, Rui
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.
PY - 2024/6
Y1 - 2024/6
N2 - We study the asymptotic behavior of the supremum Mt of the support of a supercritical super-Brownian motion. In our recent paper (Ren et al. in Stoch Proc Appl 137:1–34, 2021), we showed that, under some conditions, Mt-m(t) converges in distribution to a randomly shifted Gumbel random variable, where m(t)=c0t-c1logt. In the same paper, we also studied the upper large deviation of Mt, i.e., the asymptotic behavior of P(Mt>δc0t) for δ≥1. In this paper, we study the lower large deviation of Mt, i.e., the asymptotic behavior of P(Mt≤δc0t|S) for δ<1, where S is the survival event.
AB - We study the asymptotic behavior of the supremum Mt of the support of a supercritical super-Brownian motion. In our recent paper (Ren et al. in Stoch Proc Appl 137:1–34, 2021), we showed that, under some conditions, Mt-m(t) converges in distribution to a randomly shifted Gumbel random variable, where m(t)=c0t-c1logt. In the same paper, we also studied the upper large deviation of Mt, i.e., the asymptotic behavior of P(Mt>δc0t) for δ≥1. In this paper, we study the lower large deviation of Mt, i.e., the asymptotic behavior of P(Mt≤δc0t|S) for δ<1, where S is the survival event.
KW - Lower large deviation
KW - Super-Brownian motion
KW - Supremum of support
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U2 - 10.1007/s10959-023-01292-3
DO - 10.1007/s10959-023-01292-3
M3 - Article
AN - SCOPUS:85174484380
SN - 0894-9840
VL - 37
SP - 1079
EP - 1123
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -