【115/5/28】15:20-16:10 Prof. JYY-I HONG (Department of Mathematical Sciences, NCCU)
| Colloquium | |
|---|---|
|
|
|
| Time | 2026-5-28 15:20-16:10 |
| Venue | 31106, Department of Mathematics |
| Speaker | Prof. JYY-I HONG (Department of Mathematical Sciences, NCCU) |
| Title | Limiting Behaviors of Discounted Branching Random Walks |
| Abstract | In classical branching random walks, a population evolves through reproduction and spatial displacement, and under supercritical growth (1 < m ≤ ∞) with i.i.d. displacements, the maximal position Mn of each generation n diverges to infinity almost surely as n → ∞. This reflects an ever-expanding frontier driven by exponential or doubleexponential (super-exponential) population growth. In this talk, we revisit this paradigm from a resource-based perspective. Interpreting displacements as gains of resources and positions as accumulated wealth along ancestral lineages, we introduce a discounted branching random walk in which past gains are subject to temporal decay. This modification captures economically meaningful features such as depreciation, obsolescence, or diminishing value over time. The central question we address is whether, despite rapid population growth, the cumulative discounted resources along a lineage can remain finite. We present sufficient conditions—formulated in terms of the offspring distribution, the displacement distribution, and the discounting mechanism—under which the maximal discounted position converges in distribution or remains bounded. These results reveal a delicate balance between growth and decay: while branching promotes divergence, discounting can counteract it and lead to finite limiting behavior. This framework opens new directions for understanding long-term accumulation under competing forces of expansion and decay. |
|
|
|
