TYPOS

1. Page 5 line 4 - should be B_i instead of B_m

2. Page 11 - The proof of Cauchy-Schwarz inequality
can be done in the same way as in Thm 1.34

3.!! Page 21 -
Theorem 1.47 part 1 - should be a condition on the positivity

of probabilities
of hitting rectangles, instead of simple monotinicity

part
2 - the limit should be as at least one coordinate

tends to -\infty (not necessary for all the coordinates to tend to -\infty)

4.!! Page 32 - de Moivre-Laplace Theorem - should be (exp(
...) + \delta_n(k))

instead of exp(...)(1 + \delta_n(k)).
The same thing in two places on the next page

5. Page 36 - Problem 7 - better say: The
voting machines recorded 520000 votes for the first candidate and 480000 for
the second one.

6.! Page 36 -
Problem 8 - is there a solution in the closed form?

7. Page 56 - Problem 1 - better use the words
random variables

8. Chapter 21 - maybe need to be more careful
with the assumptions on smoothness for the coefficients of PDE's

9. Page 49 - Remark 3.25 not stated well

10. Page 64 - should be reference to (4.3)
instead of (4.4) in several places

11. Page 3 - no need for and X = \{1,...,r\} - three lines from the bottom

12. Page 50 - should be \varepsilon/5 instead of
\varepsilon - three lines from the bottom.

13. Page 51 - should be \mu_2(B)
instead of \mu_2 - 4 lines from the bottom

14. Page 54 - should be || ||_p instead of || || in two places
four lines from the bottom.

15. Page 67 - following Definition 5.1: 'This
property ... differently' - not needed.

16. Page 73 - By (5.3) and (5.4) - should be
replaced by By (5.4) - line 6.

17. Page 73 - by (5.3) should be replaced by by (5.4) - line 15

18. Page 101 - mention that Khinchin
thm is a particular case of 2-nd
Kolmogorov thm

19. Page 106 - Problem 4 - parts (a) and (b) can
be stated as one: prove that \lambda(...) = 1.

20. Page 106 - Problem 6 - shouldn't ask
for ... if and only if?

21. Page 116 - Problem 1 - What if the limit is
not a \delta-function? Maybe we should assume that the space is R or a
separable metric space.

22. Page 117 - Problem 12 - move
to the next chapter.

23. Page 125 - Remark 9.10 - confusing - need to
assume that \varphi is a char function, or, at least
is continuous at zero?

24.! Page 145 - Kramer vs Cramer (perhaps
elsewhere as well).

25. Page 189 - the first statement in the second
paragraph needs to be explained better.

26.! Page 197 -
end of the proof of Theorem 13.33 - the convergence in L^1 has already been proved
above.

27.!! Page 283 - in both definitions need to assume that X_t is progressively measurable. Need to move the
definition of progressive measurability here, also move problems 1 and 2 of the
next chapter to this one.

28.!! Page 278 Lemma 19.3 and page 283 Lemma 19.10 - need
also to consider the case when \tilde(\Omega) is the space of
continuous functions and X is a continuous process. Otherwise, an example on
page 287 does not work.

29. Page 288 - third formula - need \cal{F}
instead of F.

30.!! Page 297 - Lemma 20.12 - need continuity of A_t.

31. Page 311 - problem 8 - should be 1 instead
of t in the limit of integration.