Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students Graduate Seminar Kevin Ou Carnegie Mellon University Title: Characterize Characteristic Functions of Probability Distributions Abstract: Most probability texts give properties of characteristic functions (necessary conditions) but touch the converse (sufficient conditions) only tangentially. We will together re-discover and prove (rigorously) the most popular sufficient and necessary conditions of characteristic functions, called Bochner's Theorem (or Bochner-Khintchine in Russian texts). We then apply the theorem to two examples, one of which is the "real" Khintchine's Criterion. The related but harder moment problem may be mentioned (to motivate possible future talks).Motivations to study Bochner's Theorem and/or to attend the talk: 1. Characteristic function plays a "central" role in probability theory. 2. Construct "possibly new" probability distributions. 3. Prepare to tackle the moment problem. 4. More accessible approach to an abstract Fourier analysis theorem (Fourier analysis will only be "$epsilon \downarrow 0$", and everyone in the department is welcomed) 5. Basic exams, maybe...Date: Tuesday, September 22, 2015Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Zilin Jiang