演講者簡介 : Prof. Lin received his Ph.D. in Mathematic from Hangzhou University in 1962. He is currently a Professor of probability and statistics at Statistics Department of Zhejiang University. His research fields are classical and modern probability limit theory, sample path properties of stochastic processes and asymptotic theory of large samples.
演講摘要 : From the classical theory of weak convergence of probability measures, we introduce the Donsker theorem. In this talk, The emphasis is on the introduction of modern theory. Weak convergence of various general functionals of partial sums of dependent random variables (statistics) to stochastic integrals now plays an important role in the modern probability theory and statistical theory. We introduce the weak convergence of various general functionals of partial sums of causal processes to stochastic integrals driven by Brownian motion and various general functionals of partial sum processes of i.i.d. random variables with heay-tail to stochastic integrals driven by Levy α-stable process.
