Math 850, Fall 2007

Pasquerilla Center 105: MWF 1:55-2:45


Homework


  • Homework 9 (due Wednesday, December 5):
    Let X(t) = N(t) - t, where N(t) is the usual Poisson process. Show that X(t) and X(t)^2 - t are martingales relative to the filtration associated to N(t).
    Using the Ito calculus, find d[exp(B_t)]; find d[sin(B_t)]; and d[exp(t B_t)].

  • Homework 8 (due Wednesday, November 21):
    Do Problems 1, 2, 4 of 12.1 and Problem 1 of 12.4.

  • Homework 7 (due Wednesday, November 7):
    Do the problems on the Sample test.

  • Homework 6 (due Wednesday, October 31):
    Do Problems 1, 2, 3, 9, 12 of 6.1; and Problem 2 of 6.2.

  • Homework 5 (due Wednesday, October 17):
    Do Problems 16, 17 of 1.8; Problems 2 (skip the variance question), 8a, 9 of 5.1; Problems 1, 2a of 5.3; and Problems 1a, 2 of 5.10.

  • Homework 4 (due Wednesday, September 26):
    Do Problem 8 of 3.6; Problem 4 of 3.7; Problems 5b, 13a of 3.11; and Problems 1, 2 (assume the pdf f is continuous) of 4.2.

  • Homework 3 (due Wednesday, September 19):
    Do Problem 4, 6, 7, 19 of 2.7; Problem 1 of 3.1; Problem 4a of 3.2; and Problem 6 of 3.3.

  • Homework 2 (due Wednesday, September 12):
    Do Problem 2 (with n = 3) of 1.5; Problem 22, 34 of 1.8.

  • Homework 1 (due Friday, September 7):
    Do Problem 2, 4 of 1.2; Problems 5 of 1.3; Problem 3 of 1.4; Problem 9 of 1.5.


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