# 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 Q(phi)>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 phi (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)

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)

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 | … ) should be P_t(X_{0:t} in dx_0:t | … ) (Feras Saad)

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

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)

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)

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