A List of Errors and Misprints in
the Text by Stark and Woods
The following is a list of errors and
misprints spotted so far
in the second edition of the text by Stark and Woods that we have been
using for
this course. This list has been compiled over the years, with the
contributions
of the students who have taken the course (in particular, the class of
Fall '94)
and other instructors who have taught the course (in particular, Prof.
Ken Zeger,
who is now with UCSD).
Throughout, TEX notation has been used.
- [page 27]
In the third line of text above Eq. 1.7-7: "particles among in
cells...": "in"
should be "n".
- [page 40]
In item 2, there should be a space between "k" and "(k>1)".
- [page 54]
Misprint in Figure 2.2-1: "E_s" should be "E_b".
- [page 57]
Equation in middle of page: It might be clearer to include an
intersection
symbol in equation {X < x_1}{x_1 < X < x_2} = \phi
- [page 76]
Equation in middle of page: (-)^k should be (-1)^k.
- [page 82]
Second paragraph from bottom, first line: The cross denotes
a nonexistent footnote.
- [page 84]
Third line from top of page: "well" should be "will".
- [page 89]
Third line above Ex. 2.7-6: The closing parenthesis should instead be a
closing square bracket.
- [page 91]
Item E is missing the text: F_XY(x,y)=0.
- [page 113]
Item (i): last event at end of the first line should be {x: x<0}.
- [page 117]
Third equation above 3.2-15 should have an opening square
bracket rather than opening parenthesis.
- [page 137]
First full paragraph, third line "m>=n" should be replaced by
"m<=n".
- [page 167]
Equation middle of page following "Then": y^j_k should be replaced by
y^(j)_k .
- [page 172]
First line of definition 4.2-3: should read "Let X and Y be
continuous... "
- [page 176]
First line of text below equation below ex. 4.2-4: should
be "can also be written as E[Y]=E[E[Y|X]] . . ."
- [page 176]
In lines 4 and 5, you should replace E[Y|X(\eta)] by E[Y|X=X(\eta)]
since
the terminology E[Y|X(\eta)] has not been defined. It might be helpful
to
add a sentence like the following: "If we define the real-valued
function g(z) = E[Y|X=z] then we can
formally define the {\it conditional expectation of Y given X} as the
random
variable E[Y|X] \eqdef g(X)."
- [page 188]
8th line of text on page should read " . . . a sophisticated
algorithm called filtered . . . " i.e. call -> called
- [page 202]
Equation 4.6-4 should have a capital "P".
- [page 206]
2nd from top should has closing parenthesis which is hangs down too
far.
- [page 211]
First equation at top is missing an integral sign.
- [page 211]
Second equation from top, last integral: "-jw_2x" should be "-2jw_2x".
- [page 213]
Equation 4.7-19: Closing square bracket should be in the superscript.
- [page 215]
Change n to \sqrt{n} in the exponent under the integral in the
computation of \Phi_W^{(2)}(0) in the middle of the page.
- [page 216]
In the Taylor series expansion of \ln{\Phi_{Z_n}(\omega)} there should
be
a factor of 1/2 in front of the quadratic term and a 1/3 in front of
the cubic.
- [page 234]
First equation at top: little z should have a superscript capital "T".
- [page 240]
line of text beginning "we must find..." has typo in equation: "vPv"
should have first v in bold.
- [page 241]
Equation defining cosine of theta should have a bold letter
"a" in numerator (the transposed one).
- [page 258]
Equation 5.6-2 is missing "e" in the integral.
- [page 259]
There is an unmatched closing parenthesis in equation 5.6-4 near the
2\pi.
- [page 259]
In the 1st equation of Ex 5.6-1, the w_1, w_2, and w_3 characters
should
not be in boldface in the exponent.
In next equation, same problem with w_1, etc on the vertical bar
following
the partial derivative.
- [page 259]
Same boldface problem in equation 5.6-5 for only w_1 in vertical bar.
- [page 260]
Third line above equation 5.6-8 is missing a closing
square bracket.
- [page 262]
Equation before 5.6-20 has a mismatched opening parenthesis
with closing bracket.
- [page 264]
The equation in problem 5.2 contains a bold "P". This
"P" should not be bold.
- [page 265]
In problem 5.10 (b), last equation should read AA' = A'A .
- [page 289]
4th equation line from bottom. The double summand over i NOT EQUAL to
j.
- [page 298]
Equation for epsilon in middle of page should have "g_0(x)" rather than
"g(x)".
- [page 299]
Equation 6.7-5 is wrong somewhere. e_{min} has an "i" superscript,
which
is the running index of the sum.
- [page 300]
Equation for a_{io} in middle of page: "a_{io}" should be "a_i".
- [page 325]
2nd line from the bottom of the page: "it's" should be "its".
- [page 330]
Replace t by \tau in the exponent inside the integral.
Five lines later, "property (A) on p. 129" is mentioned but there is no
such thing on page 129 .
- [page 331]
Line of text before second set of equations in example 7.1-8:
replace "&" with "and".
- [page 331]
Last paragraph, 1st and 3rd line: "Figure 7.1-4" should be "Figure
7.1-5"
- [page 332]
Last line of first paragraph of Ex. 7.1-3: "Figure 7.1-5"
should be "Figure 7.1-6"
- [page 334]
In Definition 7.1-3 the text: X[n_2 - X[n_1,... is missing 2 right
brackets and should be X[n_2] - X[n_1],...
- [page 336]
Second line of definition 7.2-1: "X_1[n]" should be "x_1[n]".
- [page 339]
Equation 7.2-6b: The omega in the exponent under the integral
sign should not be bold.
- [page 353]
Fourth line of text in definition 7.4-6: "We sometimes write
X[n] -> X (p), where (P) denotes . . . " The "(P)" should be "(p)".
- [page 363]
Problem 7.5 (a): The equation for F_M(m) should have a "1" in place of
"l".
- [page 367]
Problem 7.16 (b) (ii): In the expression "X[n,zeta]", the
zeta is bold-faced and should not be.
- [page 367]
Problem 7.17: Last line on the page: "\geq" should be "\leq".
- [page 377]
In the summation for N(t) the lower limit should be n=1 instead of n=0.
- [page 379]
4 lines from the bottom it says "See also Problem 1.30". It should be
1.33 .
2nd paragraph 6th word "evalaute" should be "evaluate".
- [page 387]
In computing E[X_T^2 (nT)] change ns^2 to (n+1)s^2.
Two lines later change t\frac{s^2}{T} to (\lfloor\frac{t}{T}\rfloor
+1)s^2 .
- [page 389]
12 lines from the top: change "white" to "while".
- [page 406]
In the legend of Figure 8.2-3a insert "for" before "various" and remove
comma.
- [page 414]
Problem 8.5 (b): After the "P" there should be a "[" instead of a "|".
- [page 417]
Problem 8.19 (a): The equation is inconsistent in its use of
"X(0)" and "X_0". Apparently, X(0) = X_0 and only one should be used.
- [page 420]
The "only if" part of the proof of Theorem 9.1-1 is wrong. Here's a
correct
proof. Suppose the process is m.s. continuous at 0, we show that R is
continuous in a neighborhood of (0,0). Note that
X_tX_s-X_0X_0=(X_s-X_0)(X_t-X_0)+X_0(X_t-X_0)+(X_s-X_0)X_O
Take expectations of each side and use the Schwartz inequality to find:
|R(t,s)-R(0,0)| \leq ||X_s-X_0)||||(X_t-X_0)||
+||X_0||||(X_t-X_0)||+||(X_s-X_0)||||X_O||
where ||Z||=E[Z^2]^{1/2}. The RHS tends to zero as (s,t) converges to
(0,0).
It clearly follows from the same type of proof that R is continuous at
(t,t).
QED
- [page 426]
After the words "to obtain" the equation R_xx'(t_1,t_2 = lim... is
missing
a right parenthesis and should be: R_xx'(t_1,t_2) = lim...
- [page 431]
The last equation in the proof at the top of the page is
missing a closing parenthesis.
- [page 432]
In the proof of item 1, there is a typo where the norm
of A_n is defined. It should be ||A_n||= . . .
- [page 435]
In the line above equation 9.2-4b, there is a close parenthesis
missing from X^*(t_2)
- [page 436]
The first equation on the page has a typo. The close parenthesis
is missing from the upper limit on the integral.
- [page 440]
In the sixth line of the second paragraph, t_i should be t_1.
- [page 442]
1st line of the last paragraph, "&" should be replaced with "and".
2nd line of the last paragraph change "characteristic" to
"characterized".
- [page 443]
In the third line above Def. 9.4-1, "an" at end of line should be "a";
furthermore, random variable should not be abbreviated here.
(just a style suggestion...)
- [page 447]
"I" should be replaced with "1" in equation after "and then use
Parseval's theorem [9-4] to evaluate the above variance as" equation.
- [page 449]
7 lines from the bottom of the page: change "9.4-6" to "9.4-7".
- [page 452]
The 2nd and 3rd lines from the bottom are identical equations. Remove
one.
- [page 452]
4 lines from the bottom before the equal sign it incorrectly says:
E[{\hat X}(t) ((t) - {\hat X}(t))^*] It should say:
E[{\hat X}(t) (X(t) - {\hat X}(t))^*]
- [page 458]
Fact 3: should read "Either R_1(t,s) = 0 for all . . ." i.e. or ->
for
- [page 462]
A closing curly bracket is missing from the last term
in the last equation of part (b) of Problem 9.6.
- [page 469]
In the middle of the page it says "which follows directly from
E[|X(t+\tau) -X(t)|^2] \geq 0 .
For complex valued X(t) this leads to Re[R_{XX}(\tau) \leq R_{XX}(0)
which does not prove the result. Instead use the Cauch-Schwarz
inequality
to get |E[X(t+\tau)X(t)^*]| \leq \sqrt{E|X(t+\tau)|^2 E|X(t)^*|^2} =
R_{XX}(0).
- [page 479]
There seems to be a deletion of a line or so between
last line of page 479 and first line of page 480. In the 1st Edition of
the
book on page 344 the text that is missing seems to be:
"m.s. derivative of an uncorrelated increments process,"
- [page 480]
The last line of page 480 seems to be finished on the first line of
page 480
(as well as on page 481). Remove the 1st line on the top of page 480.
- [page 481]
In line 3, change "by substituting t for t-\tau" to:
"by substituting t-\tau for t" .
- [page 516]
Equation 10.6-10: A closing parenthesis is missing on the "Y(t_0)"
term.
- [page 530]
Third equation from top: Lower limit in last sum should read "n_2=-N".
- [page 542]
In Prob 10.16, replace "10.7-5" with "10.7-6".
- [page 542]
In problem 10.19, R_X(t) should be R_X(\tau).
- [page 551]
Second equation line should be K_{YX} (not K_{YK})
- [page 555]
Theorem 11.2-2 second equation line close expectation brackets after
Y_1 .
- [page 565]
In Eq. 11.4-6 change the tilde over the X to a hat.
- [page 569]
4 lines after the caption "Error-Covariance Equations" change the hat
over the first X to a tilde.
- [page 569]
In the first line of Eq 11.4-12 change the hat over the Y to a tilde
and
change X tilde [n] to be instead {\hat X} [n | n-1].
- [page 571]
In the last line of the equation before Example 11.4-1 the 2nd B should
be
transposed.
- [page 598]
Problem 11.10 (a): the first E should have a hat on it.