# Typos and errors

A lot of thanks to anyone who found the errors below (their names appear in parentheses). Feel free to contact me if you find others.

# Major mistakes

100, Exercise 8.7: the fact that the former estimator dominates the latter (in terms of asymptotic variance) is equivalent to the stated equality provided $\mathbb{Q}(\varphi)>0$ (this condition is omitted in the book). Moreover, when $w$ is an indicator function, one has equality (both estimators have the same variance asymptotically). (Otmane Sakhi)

171, Lemma 1.2: assumption that $G_t$ is upper bounded is not required. (Adrien Corenflos)

182, Lemma 11.10: this lemma is correct only if function $\varphi$ takes both positive and negative values. In the following calculations, this lemma is applied to centred functions ($\varphi$ minus its expectations). (Adam Johansen)

# Typos

41, second equation: missing $dx_{t-1}$ in the integral (Chihiro Kuraya)

44, first equation: $f_t$ should be $f_s$ (Chihiro Kuraya)

56, first equation: $M_{0:t-1}(dx_{t-1})$ should be $M_{t-1}(dx_{0:t-1}$) (Feras Saad)

59, first equation: $H_0(x_0)$ should be $H_{0:T}(x_0)$ (Feras Saad)

63, (5.17), top line: the first probability distribution should be with respect to $X_t$, not $X_{t-1};$ i.e. $P_t(X_t \in dx_t | Y_{0:t} = y_{0:t})$ (Giovanni Diana)

73, summary: mathematically equivalently -> mathematically equivalent (Feras Saad)

76, result 2 (near bottom of the page) $y_{1:t}$ should be $y_{0:t}$ in the first factor of the RHS.

92, equation below (8.5): missing sup with respect to $\varphi$ (Adrien Corenflos)

92, Theorem 8.5: [w] missing just before big closing parenthesis (Chihiro Kuraya)

116, second equation in Lemma 9.2: $V_n$ should be $V^n$ (Adrien Corenflos)

117, equation on last line: n and n - 1 should be superscripts;

also interval [n-1/N, n/N] should be [(m-1)/N, m/N] (Chihiro Kuraya)118: same issue in first multi-line equation: replace $n$ by $m$ in the interval $[n-1/N, n/N]$, and below the sum (second line). (Chihiro Kuraya)

119^4 (display in proof of Prop 9.4): $W^n$ should be $W$. (Chihiro Kuraya)

119_5: estimate(d) -> estimates (Adrien Corenflos)

122, Ex 9.10: the first constraint is $E(W)=x$ (missing “=x”). (Omiros)

126: Guldas et al (2017), “volume 28” -> “volume 48, Issue 28”. (Feras Saad)

130, Algorithm 10.1: resampling step should be based on weights $W_{t-1}^{1:N}$, not $W_t^{1:N}$ (Chihiro Kuraya)

131, grey box: space missing after “approximates”. (Omiros)

139, first box, 3rd bullet: “P_t » M_t”, should be the reverse: “P_t « M_t”; also, $P_t(X_t \in dx_{0:t} | \ldots )$ should be $P_t(X_{0:t} \in dx_{0:t} | \ldots )$ (Feras Saad)

139: the following Radon-Nykodym derive (s) exist (Adrien Corenflos)

144, last line of Example 10.5: the second term should be $\sigma^2[y_t^2 e^{-\mu^\star(x_{t-1})} - 1] /2$ (Gonzalo Mena)

152, (10.4): missing tilda on the $X_{t-1}$ in the second term.

176: Proposition 11.2 should be Proposition 11.5. (Adam Johansen).

180, snd line of Lemma 11.7: $\phi$ should be $\varphi$ (Chihiro Kuraya)

190: in both lines below the display, h should be k in $z_{t-1}$ (Suzie Brown)

195, Algorithm 12.1: functions $\Phi_0^n$ and $\Phi_t^n$ should read $\Phi_0^N$ and $\Phi_t^N$; i.e. we compute recursively $\Phi_t^N(X_t^n)$. (Mathieu Gerber)

239: in the 9th line of Alg 13.3, $H_{t-1}^{1:N}$ should be $H_t^{1:N}$ (Chihiro Kuraya)

258: $\theta^{n-1}$ should be $\theta_{n-1}$ in function $\theta$ -> $Q(\theta, \theta^{n-1})$ (Feras Saad)

264, second displayed equation: last product should be from $t=0$ to $T$ (not $t$)

267, (14.9): replace $\theta$ by $\theta_{n-1}$ in the gradient

282, first line: give(n) proposal (Adrien Corenflos)

$283

*8$: $O(d^2)$ should be $O(d*\theta^2)$ (Feras Saad)285, 4th line before Sec 15.5: full conditional should be $q_k(\theta(k)|\theta(-k))$ rather than $q(\theta(k)|\theta(-k))$ (Chihiro Kuraya)

287, caption of Fig. 15.2: (t)he first $10^5$ simulations

295, Example 6.1: better behaved tha(n) (Feras Saad)

300, Prop 16.1: missing tilde on the $M$ of the proposed kernel (Feras Saad)

301^1: $(z/c)$ instead of $(Z/c)$ in the expression of $L(\theta, z)$ (Chihiro Kuraya)

332, second paragraph of 17.2.1: covariance matrix should be set to $\lambda^2\hat{\Sigma}_{t-1}$; note the missing square (Mathieu Gerber) In fact, $\lambda$ should be replaced by $\delta$ on that page, since that quantity was denoted by $\delta$ in Chapter 15, and since letter $\lambda$ means something else in the rest of the chapter (the tempering coefficient).

337, Algorithm 17.3, second line of the else block: replace $\Theta_t^n$ by $\Theta_{t-1}^{A_t^n}$ (Adrien Corenflos)

342, (17.5): $p_t^\theta$ should be $p_T^\theta$