Math 5652: Homeworks

Homework rules: Submitted work must be your own. You are allowed and are enouraged to discuss some points of the problems with another student in the class.
However you must write each problem on your own, and you are required to write the name of the student you have discussed problems with at the beginning of each assignment.

All the homework numbers refer to problem numbers in the text "Essentials of Stochastic Processes" by R.Durrett, Springer(1999).
  • Hw 1 (Ch probability review):
    1.28, 2.18, 3.16, 3.28, and a, b, c in Homework 1

  • Hw 2 (Ch 1-Markov chains):
    9.2, 9.8, 9.22, 9.32, 9.46, 9.48 and a in Homework 2

  • Hw 3 (Ch 2-Martingales):
    4.1, 5.13, 5.19, 5.20 and a in Homework 3
    corrections in statements of 5.19 (b): Use (3.6);   5.20 (a): Show that g(X_min(V,n))+min(V,n) is a martingale;  5.20 (b): all x in B

  • Hw 4 (Ch 3-Poisson Processes): 7.8 (a)-only, 7.18, 7.22, 7.28

  • Hw 5 (Ch 4-Continuous-time Markov chains): 8.4, 8.16, and a, b, c in Homework 5

  • Hw 6 (Ch 6-Brownian motion): 6.1, 6.8, 6.18 and a in Homework 6