Special Session 191: Stochastic Dynamical Systems Under Levy Noise: Theory and Applications

Local and Global Solutions for Stochastic Transport-Type Equations with Nonlocal Noise
Yingting Miao
Xi'an Jiaotong-Liverpool University
Peoples Rep of China
Co-Author(s):    
Abstract:
This presentation discusses results on stochastic transport-type equations driven by genuinely mixed multiplicative noise. The noise comprises a continuous component (interpreted in both the Stratonovich and It\^{o} senses) and a discontinuous component (interpreted in the Marcus sense). The Stratonovich and Marcus noise amplitudes are given by (nonlocal) pseudo-differential operators, which include the classical transport operator as a special case. Within this setting, we establish the existence, uniqueness, and a blow-up criterion for pathwise classical solutions. We further prove that sufficiently fast-growing noise ensures global regularity.