Introduction to stochastic calculus

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

• Syllabus : see here

• Schedule : Wednesday 8.45 - 10.15 in room 309 of the math building
  

• Class dates :
  April 10, 17, 24
  May 1, 8, 15, 22, 29
  June 5, 12, 19, 26
  July 3, 10
  

• Program :
  Mathematical Background
  Stochastic processes
  Brownian motion
  Stochastic integrals
  Itô processes and stochastic differential equations
  Markov processes
  Applications to finance
  

• Lecture notes : Stochastic calculus
  

• 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.

• Works submitted by students :
  Brownian motion in free probability theory, by Hyuga Ito
  Probability theory, by Risan
  Mathematical background, by Cunyi Nan
  Gaussian process, by Cunyi Nan
  Conditional probability and conditional expectation, by Cunyi Nan
  Martingales, by Cunyi Nan
  Brownian Process, by Risan
  Elaboration of ''enumerating graphs and Brownian motion'', by Risan
  Stochastic calculus exercises, by Risan
  Some problems on Itô calculus, by Nguyen Duc Thanh
  Gambler's ruin, by Qiuling Low
  Self-financing trading strategy, by Qiuling Low
  

• 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