Dynamical systems arising in engineering and science are often subject to random influences("noise").The noisy processes may be non-Gaussian,which are modeled by α-stable Levy motions.Non-Gaussianity of the noise manifests as nonlocality at a "macroscopic" level.To understand dynamics under uncertainty,deterministic quantities that carry dynamical information are examined.These quantities include "escape probability","mean exit time" and "probability density functions",leading to considerations of deterministic nonlocal partial differential equations(PDEs).In the context of Fourier transform,the nonlocal term in these partial differential equations is related to the nonlocal Laplacian operator.In other words,better understanding of nonlocal PDEs would be beneficial for understanding stochastic dynamics.The speaker will first present an overview of certain techniques for investigating non-Gaussian stochastic dynamics,highlighting the need of harmonic analysis for nonlocal PDEs.