Stochastic Processes

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Revisão de 09h03min de 10 de maio de 2018 por V1z (discussão | contribs) (Software)

This is the main page of an undergraduate-level course in stochastic processes, being taught in 2018 (2017 semester 2) 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

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

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


Partial listing



  • P1 (easy): 2012 2018
  • P2 (harder):
  • Final-Sub:

Evaluation criteria

     M_p = (P1 + P2)/2   
     M = 0.8*M_p + 0.2*T (atualizado de 10% para 20% com acordo dos alunos), onde T é a nota dos trabalhos
     Se M >= 5, passou --> M (facilitando: considere T=10,0 no M `a esquerda desta desigualdade aqui)
     prova final - faz quem quiser, mas combinamos que teria de seria feita por quem obtiver M < 5 
    M_f = 0.5*(M + P_f) = 0.5*(0.8M_p + 0.2*T + P_f) = 0.2*P1 + 0.2*P2 + 0.5*P_f + 0.1*T
     Se M_f >= 5, passa --> M_f
     Sub: repoe menor de P1, P2, P_f (apenas se alguem faltou alguma prova ou quiser melhorar nota - mas quem entregar ira substituir)
     M_sub = media com sub
     Se M_sub >= 5, passou --> M_sub
     Adendo (em acordo com os alunos): a M_sub = M_f pois sera considerada a mesma prova. Quem for usar a prova como Sub ira substituir a nota independentemente do resultado.