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Last updated:

November 3, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This class covers the analysis and modeling of stochastic processes.

Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models

Course Curriculum

  • Metric spaces Unlimited
  • Large deviations technique Unlimited
  • Cramér’s theorem Unlimited
  • Applications of large deviations Unlimited
  • LD in many dimensions and Markov chains Unlimited
  • Intro Brownian motion Unlimited
  • Brownian motion Unlimited
  • Quadratic variation Unlimited
  • Filtration and martingales Unlimited
  • Martingales I Unlimited
  • Martingales II Unlimited
  • Additional materials: Martingale convergence theorem Unlimited
  • Martigales concentration inequality Unlimited
  • Talagrand’s concentration inequality Unlimited
  • Ito calculus Unlimited
  • Ito construction Unlimited
  • Ito integral Unlimited
  • Ito process and formula Unlimited
  • Ito applications Unlimited
  • Weak convergence Unlimited
  • Tightness of measures Unlimited
  • Reflected Brownian motion Unlimited

About the instructor

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Courses

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Students

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Massachusetts Institute of Technology