### Errata

• p.7 : Theorem 1.2.4, remove the word ”adapted”.
• p.$$32_1$$: $$T$$ should be $$\bf{T}$$ (bold) .
• p.$$34^{10}$$: $$X(n)^2$$ should be $$X^2(n)$$ .
• 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.$$139^2$$: 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.$$156^{6}$$: 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.$$312^{14}$$: 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.$$438_{10}$$: $$(\theta_1,...,\theta_p)$$ 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.$$718_5$$: $$\lambda_1^m\lambda_2^m\cdots\lambda_m^m \mu_1^r\mu_2^r\cdots\mu_r^r$$ 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 $$\bf{A}=\bf{P}\bf{J}\bf{P}^{-1}$$ .