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PRODID:-//prob.tw//NTU Seminars V2//EN
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UID:2025-10-20-xiaowen-zhou-an-introduction-to-diffusion-processes@seminars.prob.tw
DTSTAMP:20261014T103317Z
DTSTART:20251024T020000Z
DTEND:20251024T040000Z
SUMMARY:An Introduction to Diffusion Processes
DESCRIPTION:周曉文 (Xiaowen Zhou)\nIn this short course on diffusion processes\, we will first go over basic facts on Brownian motion\, stochastic integral and Ito's formula\, and then introduce diffusion processes as solutions to stochastic differential equations driven by Brownian motion. The last part of this course is an introduction of recent work on threshold diffusions\, which solve the stochastic differential equations with step-function drift and diffusion coefficients.\n\nOutline & Descriptions\nLecture 1: Brownian motion as a Gaussian process\, as a Markov process and as a martingale\, the zero set of Brownian motion\;\nLecture 2: stochastic integral\, Ito’s formula and stochastic differential equations\;\nLecture 3: basics of diffusion processes\, threshold diffusion and its exit problem\, potential measure and transition density.\n\nReferences\n1. Richard Durrett (1996): Stochastic Calculus: A Practical Introduction. CRC Press.\n2. Gregory F. Lawler (2006): Introduction to Stochastic Processes. Chapman & Hall/CRC.
LOCATION:台大次震宇宙館 505 室
URL:http://127.0.0.1:8123/?event=2025-10-20-xiaowen-zhou-an-introduction-to-diffusion-processes
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