5. Donsker's Theorem and Brownian Motions | Stochastic Analysis

Stochastic Analysis in Finance and Economics Links: ✅ Materials: https://tinyurl.com/stochastic-docs ✅ Video-playlist: https://tinyurl.com/stochastic-playlist Contact: ☑️ Email: cserna ⓐ econ.uni-frankfurt.de ☑️ Telegram: https://t.me/bcserna ☑️ Instagram:   / dr.bcc   ☑️ Subscribe: https://t1p.de/cserbal-sub 0:00:00 Intro 0:00:10 Content 0:02:14 Random walks 0:04:22 Moments of random walks 0:07:45 Asymptotics of random walks 0:19:22 Representation of sums 0:25:47 Expectation of sample means 0:29:52 Variance of sample means 0:37:42 Expectation of 2nd sample moments 0:45:11 Expectation of sample variance 0:50:44 Inconsistency and absence of asymptotic normality 1:07:07 Diffusively rescaled random walk 1:16:30 Properties 1:30:34 Paths 1:43:31 Donsker's theorem 1:53:30 Brownian motions 1:58:45 Limits