Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

Introduction to stochastic calculus (Fall 2023)

Registration code : 0063621
Schedule : Wednesday (18.30 - 20.00) in room 207 of Science building A

• Syllabus : See here

• SML official rule : See here

• NU EMI : Link to the website

• Class dates :
  October 4, 11, 18, 25
  November 1, 8, 15, 22, 29
  December 6, 13, 20
  January 10, 17
  

• Program (tentative):
  Basic notions of probability
  Gaussian processes
  Brownian motion
  Martingales
  Itô calculus
  Stochastic differential equations
  Applications to finance
  

• Lecture notes:
  The cumulative notes, updated on a regular basis
  

• Weekly summaries : 1, 2, 3, 4, 5, 6, 7, 8,

• Study sessions : Will be organized on an individual basis by some students.

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Vic Austen.

• Works submitted by the students :
  Complements and unions imply intersections, by Yat Ming Luk
  Complements and unions imply intersections: II, by Ai Yamada
  Three pairwise i.i.d. random variables that are not i.i.d., by Rasmus Skadborg
  Simple properties of a measure, by Hadiko Rifqi Aufa Sholih
  Simple properties of a measure, by Uyanga Khoroldagva
  On the power set of a finite set, by Hevidu Samarakoon
  On independence, by Ziyu Liu
  On probabilities and continuity of probabilities, by Yuu Hiramatsu
  Power set of a set of N elements, by Masumi Okamoto
  On densities and conditional expectation, by Rasmus Skadborg
  Proof of Markov's inequality, by Tran Le Phuong Quynh
  Example of a Brownian motion, by Ai Yamada
  Gaussian vector of standard Gaussian distributions, by Uyanga Khoroldagva
  The conditional expectation: a bounded operator in L^p-spaces, by Tue Tai Nguyen
  Why normal distribution's integral is 1?, by Qiuling Low
  1-dimensional Brownian processes are Gaussian processes, by Rafi Rizqy Firdaus
  

• References : (electronic version available upon request)
  [A] J.-L. Arguin, A first course in stochastic calculus
  [B] P. Baldi, Stochastic calculus, an introduction through theory and exercises
  [D] R. Durrett, Stochastic calculus, a practical introduction
  [E] L.C. Evans, An introduction to stochastic differential equations
  [K] F. Klebaner, Introduction to stochastic calculus with applications
  [Ku] H.-H. Kuo, Introduction to stochastic integration
  [M] T. Mikosch, Elementary stochastic calculus with finance in mind
  [SP] R. Schilling; L. Partzsch, Brownian Motion: an introduction to stochastic processes