報告題目：Two Sides of Noise: Good and Bad

報告人： 毛學(xué)榮 教授 英國思克萊德大學(xué)

報告時間：2025年7月17日上午8:30-9:30

報告地點：kaiyun開云官方網(wǎng)站犀浦校區(qū)X30456

報告摘要：One of the important problems in many branches of science and industry, e.g., pandemic, ecology, biology, engineering, finance, social science, is the specification of the stochastic process governing the behaviour of an underlying quantity. We here use the term {\it underlying quantity\/} to describe any interested object whose value is known at present but is liable to change in the future. In this talk we will explain how the ordinary differential equations (ODEs) are not enough to model the underlying stochastic quantity and why stochastic differential equations (SDEs) appear naturally. Several well-known SDE models will be presented including the Nobel prize winning model in finance, stochastic SIS epidemic model, stochastic Lotka-Volterra model in population dynamics. We will then explain how SDE models differ significantly from ODE models and reveal two sides of noise: good and bad. We will highlight how we can make use of noise in various applications including stochastic stabilisation, volatility effect in finance, population explosion suppressed by noise, extinction of infected individuals by noise in epidemic while we will also point out the destabilisation effect of noise.

報告人簡介：英國思克萊德大學(xué)數(shù)學(xué)與統(tǒng)計系教授、愛丁堡皇家學(xué)會（即蘇格蘭皇家學(xué)院）院士、“英國沃弗森研究功勛獎”獲得者。他是國際知名的隨機穩(wěn)定性和隨機控制領(lǐng)域的專家，在該領(lǐng)域做出了杰出的貢獻。他擅長隨機分析、隨機系統(tǒng)數(shù)值計算，在隨機系統(tǒng)處理方面，提出了系列處理方法與技巧，被廣泛采用。例如，對噪聲鎮(zhèn)定給出了科學(xué)的理論，被后續(xù)跟蹤者所廣泛推崇；在隨機人口以及疾病模型理論方面做出了突出的貢獻；在隨機系統(tǒng)LaSalle原理方面做出了開拓性的工作；奠定了隨機跳變系統(tǒng)理論方面的研究。