Probability II


  • Instructor: Prof. Ioannis Karatzas
    • 4:10-5:25pm on TuTh, 312 Math
    • TA: Tomoyuki Ichiba
      • email: ichiba -at- stat d0t columbia d0t edu
      • Recitation: Tue 8:00-9:00 PM, location is at room 307 Math.
      • Office hour: Tue 9:00- PM. location is at room 307 Math
    • Mid-term Exam: 13 March.
    • ROOM CHANGE: Thu 27 March only Room 622(possibly Room 507)
    • Final exam: Tue 13 May 4:10-7:00 Math 312.
    • The last day of class is Thu 1 May Tue 6 May(make up date) at 4:10-5:25 Math 203.
    • There will be memorial for Minghui YU in the Low Library rotunda 25 April noon.

Downladable Course Materials

Notices and Announcements

  • Notes 1.8 was updated. (22 Jan.)
  • On 25 Jan this Friday only we have a recitation at 3:00-4:00. The location will be tentatively at room 903 in the school of social work building. at room 520 Math. We cover 8.3-8.6 in the section 2.8.(22 Jan.)
  • Notes 2.8 was posted. (23 Jan.)
  • Notes 4.1 was posted. (25 Jan.)
  • Recitation on 29 Jan: review of the final of Probability I class last semester.
  • The final of Probability I class last semester was posted.
  • Notes 4.1 was updated. (29 Jan.)
  • Notes 4.1 was updated. (31 Jan.)
  • Recitation on 5 Feb: Exercise 1-6 of Notes 4.1.
  • Notes 4.2 was posted. (5 Feb.)
  • Notes 4.1 and Notes 4.2 were updated. (7 Feb.)
  • Mid-term exam will be held on 13 March.
  • Recitation on 12 Feb: Applications of Convergence theorems and Lebesgue decomposition.
  • Notes 4.2 was updated. (12 Feb.)
  • Recitation on 19 Feb: Exercises in Notes 4.2.
  • Notes 4.3 was posted. (19 Feb.)
  • Notes 4.3 was updated. (21 Feb.)
  • Recitation on 26 Feb: Exercises in Notes 4.3 including 4.3.3.
  • Notes 4.5 and a paper on equivalent martingale measures and no-arbitrage were posted. (26 Feb.)
  • The Midterm of Probability II class last year was posted.(2 March)
  • Notes 1.6 and note on Kolmogorov-Censov Theorem were posted. (3 March)
  • Recitation on 4 March: Exercises in Notes 4.5 and 4.3.10.
  • Notes 2.9 was posted. (6 March) The mid-term will cover everything including this material (there will be no posting of additional material before the mid-term).
  • Recitation on 11 March: Exercises 9.10-9.13 in Notes 2.9.
  • ROOM CHANGE only on Thu 27 March Room 622(possibly Room 507)
  • Final exam will be held on 13 May 4:10-7:00.
  • Recitation on 25 March: Exercises 9.9 and other exercises in Notes 2.9.
  • Notes 2.9 was updated. (28 March)
  • Paper by Monroe was posted. (30 March)
  • Recitation on 1 April: Exercises in Notes 2.9.
  • Notes 4.4 was posted. (1 April.)
  • Papers by Azema and Yor, Chacon and Walsh were posted. (4 April)
  • Recitation on 8 April: Exercises related to Skorohod embedding.
  • Notes 2.7 was posted. (8 April.)
  • Recitation on 15 April: Exercises related to Large Deviation.
  • Notes on Weak convergence was posted. (15 April.)
  • Recitation on 22 April: Exercises related to weak convergence.
  • Notes 2.5, 2.9, 3.4 were updated. (24 April.)
  • Notes on Feynman and Kac was posted. (24 April.)
  • Final EXAM from last year was posted. (24 April.)
  • Notes on Lindeberg-Feller Theorem was posted. (29 April.)
  • Recitation on 29 April: Exercise 2.9.22, 2.9.26 and related exercises.
  • Recitation on 1 May: Problem solving session from the final exam last year.
  • Recitation on 6 May: Exercise from Optimal stopping.
  • Notes 4.6 was posted. (6 May.)