{"id":"hexagon/2610.00684","pdf":"https://hexagonmath.org/pdf/2610.00684v1","url":"https://hexagonmath.org/abs/2610.00684v1","tags":["msc:60H10","msc:60J76","Lévy processes","algebraic folds","boundary accessibility","killed jump diffusions","stochastic differential-algebraic equations"],"score":0,"title":"Curvature-Induced Killing at Stochastic Algebraic Folds","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Zhenyu Sun"],"reviews":0,"subject":"math.PR","summary":"We study the lifetime of a regular algebraic branch under continuous forcing and infinite-activity tangent jumps. For a parabolic fold, a first-order tangent kick decreases the discriminant by an exact quadratic amount. Symmetric stable marks of index $\\alpha\\in(0,2)$ therefore generate a one-sided normal jump kernel of index $q=\\alpha/2$, with a coefficient determined by curvature. The normal diffusion and jump amplitudes depend on the evolving tangential state. We compute the full killed generator on powers of the discriminant and obtain occupation and terminal-jump bounds for this same…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}