Errata

p.7 : Theorem 1.2.4, remove the word ”adapted”.
p.\(27_1\): "irreducible" should be "irreducible and aperiodic”.
p.\(31_{12}\): "columns" should be "rows”.
p.\(32_1\): \( T \) should be \(\bf{T} \) (bold) .
p.\(34^{10}\): \( X(n)^2 \) should be \(X^2(n) \) .
p.\(36^{6}\): \( X\) should be \(\tau \) .
p.\(119_{7}\): \( e^{\mu x -\frac{1}{2}\frac{\mu^2}{\sigma^2}t} \) should be \( e^{\mu x/\sigma^2 -\frac{1}{2}\frac{\mu^2}{\sigma^2}t} \) .
p.\(120^{5}\): \( Z_T \) should be \( M_T \) .
p.\(120^{5}\): The rest of the page: interchange the meaning of \( x \) and \( z \) except for \( f_t(x,z)\) where they are correctly placed.
p.\(120^{7}\): \( e^{-\mu x/\sigma^2} \) should be \( e^{\mu x/\sigma^2} \) .
p.\(120_{3}\): \( \sqrt{\frac{a}{b\pi}} \) should be \( \sqrt{\frac{a\pi}{b}} \) .
p.\( 133_{13}\): "columns" should be "rows"
p.\( 139^2\): Remove \( \bf{e} \) from the infinite sum.
p.145: Formula (3.11), \(S_k\) should be \(S_{k:n}\).
p.\(149^{6}\): In the phase-type representation, last row of the subintensity matrix should be \(\frac{3}{2}\) and \(-\frac{3}{2}\) instead of \(\frac{3}{4}\) and \(-\frac{3}{4}\) .
p.\(151^{6}\): \( i \) should run from \( i=0\) and not \(i=1\).
p.\(156^{6}\): nonincreasing should be nondecreasing.
p.161: Lemma 3.3.7.: \(X_i\)’s and \(X\) should not be assumed absolute continuous.
p.161: line 2,7 from bottom: should be \(F_X\) instead of \(F\).
p.171: lines 11 and 14: \(\frac{1}{2\pi}\) should be \(\frac{1}{2\pi i}\).
p.211: Example 4.2.3, Denominator should be \( (1+\theta)^3 \) and not \( (1+\theta)^2 \).
p.\(301_{1}\): Replace \( U(T) \) by \( U(T)-1 \) .
p.\(312^{14}\): Replace symbol \( F_0 \) by \( G \) .
p.\(316_{11}\): Replace symbol \( z^{\mbox{min}}(n)\) and \( z^{\mbox{max}}(n)\) by \( z_h^{\mbox{min}}(n)\) and \( z_h^{\mbox{max}}(n)\) .
p.\(319^{4}\): Replace \( \bar{F}(x+y) \) with \(\int_{x+y}^\infty \bar{F}(s)ds \).
p.\(319^{13-14}\): Replace \( F \) with \( \bar{F} \).
p.\(323^{9}\): Second term, first inequality, \( 2 \) should be \( 1 \).
p.\(324^{6}\): All terms with \( T_{N(t)+1} \) should be \( T_{N(t)} \) instead, the interarrival in progress at time \( t \).
p.\(362^{12}\): \( \tau_- \infty \) should be \( \tau_- < \infty \).
p.\(366^{8}\): \( G_+^n \) should be \( G_+^{*n} \) .
p.\(366_{4}\): \( x<\infty \) should be \( |x| < \infty \).
p.\(383\): Example 6.3.5 is rather messed up. Where it say "claim surplus" is should say "risk reserve", and consequently the meanings of \( U_n \) and \( T_n \) should be interchanged. From line \( 383_6 \) onwards should be deleted. It can be used that \( -X_{n-i+1} \stackrel{d}{=} -X_i \) to conclude that the risk-reserve process is dual to a queueing process, where the service times are the claims and interarrivals in the queue equals the premium rate times the interarrivals in the risk process.
p.\(438_{10}\): \( (\theta_1,...,\theta_p) \) should be \( (\theta_1,...,\theta_n)^\prime \).
p.\( 453_{13}\): \( \exp \left( - \lambda _ { 1} y _ { 1} + \lambda _ { 2} y _ { 2} + \lambda _ { 12} \max \left( y _ { 1} ,y _ { 2} \right) \right) \) should be \( \exp \left( - \lambda _ { 1} y _ { 1} - \lambda _ { 2} y _ { 2} - \lambda _ { 12} \max \left( y _ { 1} ,y _ { 2} \right) \right) \)
p.480: Exercise 8.5.30, Condition in \(f(y_1, y_2)\) should be \(y_1, y_2 \geq 0\) and not \(y_1 \geq y_2 \geq 0\).
p.\(485^3\): \( \tau_i(0) \) should be \( \tau_i(1) \) .
p.\( 485^7\): \( n=0,1,... \) should be \( n=1,2,... \) .
p.\( 485^{18}\): "embedded random walk" should be "embedded Markov chain".
p.620: \(\bf{T}^+\) should be \(\bf{T}^{+−}\).
p.620: Theorem 11.4.1 and proof: replace all \(O(\cdot)\) by \(o(\cdot) \).
p.623: Theorem 11.4.3 and proof: replace all\(O(\cdot)\) by \(o(\cdot) \).
p.\(718_5\): \( \lambda_1^m\lambda_2^m\cdots\lambda_m^m \mu_1^r\mu_2^r\cdots\mu_r^r \) should be \( \lambda_1^r\lambda_2^r\cdots\lambda_m^r \mu_1^m\mu_2^m\cdots\mu_r^m \) .
p.\(713^3\) \( \bf{A}=\bf{P}\bf{J}\bf{P} \) should be \( \bf{A}=\bf{P}\bf{J}\bf{P}^{-1} \) .