Solutions for Chapter 2

  1. 2.1 Then, b03-math-0282, b03-math-0283, and b03-math-0284.
  2. 2.2.a By definition of stopping times, b03-math-0285 and b03-math-0286 belong to b03-math-0287. Thus, by definition of the b03-math-0288-field b03-math-0289,
    equation
  3. also belong to b03-math-0291, and b03-math-0292 and b03-math-0293 are also stopping times. Moreover,
  4. where , and can be written as so that . Hence, , and thus, is a stopping time.
  5. 2.2.b If and ...

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