Julien Poisat


Maître de conférences / ~Assistant professor
Mathématiques / Mathematics
Section CNU : 26

Polycopié du cours de probabilités 2 de L2 - Deuxième semestre - Version 2020-2021.
Lecture notes on jump processes M2 - 2021-2022.
Nov. 15 - Compound Poisson process, random Poisson measure.
Nov. 18 - Correction of Exercises 1, 3 and 4.
Nov. 22 - Compensated Poisson measure, infinite divisibility, Lévy process.
Nov. 25 - Correction of Exercises 10 and 12.
Nov. 29 - Lévy-Itô decomposition, subordinators. Predictability.
Dec. 2 - Correction of Exercise 26 (construction of the Lévy-Itô stochastic integral).
Dec. 6 - Itô's formula. Exercise 28.
Dec. 9 - Questions 1 to 6 on p.17 (Proof of Theorem 6.1).
Dec. 13 - Doléans-Dade exponential and exponential martingales. (The triangular inequality in (A.73) is not correct). Correction of Exercise 30.
Jan. 3 - Merton model. Brief introduction to Hawkes processes. (Knowledge of Section 9 is not required for the exam).

Solutions:
[Section 1] [Section 2] [Section 3] [Section 4] [Section 5] [Section 7] [Section 8]

Annales:
[2019-2020] [2020-2021]