Stochastic Processes

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Revisão de 10h04min de 10 de maio de 2018 por V1z (discussão | contribs) (Additional books used in the course)

This is the main page of an undergraduate-level course in stochastic processes targeted at engineering students (mainly computer engineering and its interface with mechanical engineering), being taught in 2018 semester 1 at the Polytechnic Institute IPRJ/UERJ.

  • Course pages for previous years: 2012
Recent application of Gaussian stochastic processes for 3D motion capture transfer (CVPR 2017)

  • Application to path planning for autonomos cars (see this)
  • Application to robot path planning with obstacles (see this)

General Info

  • Instructor: prof. Ricardo Fabbri, Ph.D. Brown University
  • Meeting times: Tuesdays 1:20pm-3:10pm Thursdays 1:20pm - 3:10pm, room (?)
  • Forum for file exchange and discussion: email and IRC #labmacambira for chat
  • Linguagem de pro


  • Undergraduate-level mathematics and probability (will review as needed)
  • Desirable: Intermediate programming experience with any numerics scripting language such as Scilab, Python, R or Matlab. Knowing at least one of them will help you learn any new language needed in the course.


The R programming language and data exploration environment will be used for learning, with others used occasionally. The student can also choose to do his homework in Python, Scilab, Matlab or similar languages. The R language has received growing attention, specially in the past couple of years, but it is simple enough so that the student can adapt the code to his preferred language. Students are expected to learn any of these languages on their own as needed, by doing tutorials and asking questions

Approximate Content

This year's course will focus on a modern approach bridging theory and practice. As engineers and scientists, you should not learn theory here without also considering broader applications. Recent applications in artificial intelligence, machine learning, robotics, autonomous driving, material science and other topics will be considered. These applications are often too hard to tackle at the level of this course, but having contact with them will help motivate the abstract theory. We will try to focus on key concepts and more realistic applications than most courses (that come from the 1900's), that will prompt us to elaborate theory.

Main Resources


Main book

Introduction to Stochastic Processes with R, Robert Dobrow, 2016 (5 stars on Amazon) Book-R.jpg

Additional books used in the course

Learning stochastic processes will require aditional books, including more traditional ones:

  • Markov Chains: gibbs fields, monte carlo simulation and queues, Pierre Bremaud
  • An Introduction to Stochastic Modeling, Taylor & Karlin
  • Pattern Theory: The Stochastic Analysis of Real-World Signals, David Mumford and Agnes Desolneux - the first chapters already cover many types of stochastic processes in text, signal and image AI Mumford-book.jpg
  • My own machine learning and computational modeling book draft, co-written with prof. Francisco Duarte Moura Neto and focused on diffusion processes on graphs like PageRank. There is a probability chapter which is the basis for this course. We have many copies at IPRJ's library.

Other books to look at

Basic probability and statistics

  • I recommend you review from the above books. They all include a review. But you might have to see:
  • Elementary Statistics, Mario Triola (passed down to me by a great scientist and statistician)

Interesting books

  • R for data science, O'Reilly (#1 data science bestseller on Amazon) R-oreilly.png

Machine Learning

  • Pattern Theory: From Representation to Inference, Ulf Grenader


Partial listing



  • P1 (easy): 2018
  • P2 (harder):
  • Final-Sub:

Evaluation criteria

     M_p = (P1 + P2)/2   
     M = 0.8*M_p + 0.2*T, where T is homework 
     If M >= 5, pass --> M
     Pf - final exam, must be done by whoever gets exam score M_p < 5 
     M_f = 0.5*(M + P_f)
     If  M_f >= 5, pass with M_f
     Sub: replaces smallest of P1, P2, P_f (only if someone misses class or wants to improve scores - whoever hands it in, will have the grade substituted as such)
     M_sub = final grade with Sub
     If M_sub >= 5, pass --> M_sub
     For simplicity, M_sub = M_f will be considered the same exam. Whoever uses it as Sub will have the grade substituted independently of the result.ente do resultado.