List Of Typos In Chapter 5

p159 1st paragraph: "In this chapter we will introduce a class of process" -> "In this chapter we will introduce a class of processes" [Andrea Liu]

p161 in the definition of martingale, M_n should be adapted (i.e., there are functions f_n such that M_n = f_n(M_0,X_0,…,X_n))

p161 "in passing from the random variables X_n that are driving the process TO the martingale M_n" (the word "to" is misplaced)

p163 Example 5.6: "In particular, if φ(θ) = 1 then φ(θSn) is a martingale." should be: "In particular, if φ(θ) = 1 then exp(θSn) is a martingale." [Lucas Chang]

p164 Lemma 5.8: "Othogonality of martingale increments" should be: "Orthogonality of martingale increments" [Lucas Chang]

p166 Example 5.7: "means a total winning" -> "means total winnings" [Andrea Liu]

p167 Proof of Theorem 5.12: "The change in our wealth from time n to time n + 1 is Wn+1 − Wn = Hn+1(Yn+1 − Yn)" should be: The change in our wealth from time n to time n + 1 is Wn+1 − Wn = Hn+1(Mn+1 − Mn) [Lucas Chang]

p168 1st paragraph: "To quickly derive the exist distribution" -> "To quickly derive the exit distribution" [Andrea Liu]

p168 bad martingale: "we know that P_1(T<\infty) = 1" (the =1 is left out). Also the formula for V_a should have S_n=a instead of S_n=0.

p171 Example 5.13: "Theorems 5.13 and 5.11 gives" -> "Theorems 5.13 and 5.11 give" [Andrea Liu]

p172 Lemma 5.18, last displayed equation of the proof, the first equality EX_0 = EX_n should be >=.

p173 1st full paragraph: "we note that There are 2 balls". Need parentheses around (j+1), (j+2) and (n+1) in the denominator.

p174 1st paragraph: missing a left curly brace and an "n". [Bryan Chong]

p175 Exercise 5.6 Original: "Yn=UnUn-1…U0" => Should be: "Yn=UnUn-1…U1" [Mingwei Tian]

p175 Exercise 5.6 Original: "(1/n) log Xn -> -1" => Should be: "(1/n) log Yn -> -1" [Mingwei Tian]

p177 5.14, line 3: space between phi and "then". [Bryan Chong]

page revision: 14, last edited: 17 May 2013 17:48