Special Mathematics Lecture
Contact:
Serge Richard (richard@math.nagoyau.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

SML official rule :
See here

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

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^pspaces, by Tue Tai Nguyen
Why normal distribution's integral is 1?, by Qiuling Low
1dimensional 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
Back to the main page