Differential Equations Driven by Rough Paths 

by Terry J. Lyons

Lecture notes by Michael J. Caruana and Thierry Lévy

Errata


 This page makes an inventory of the mistakes that readers have spotted in the book. You can also download the errata as a pdf file. Please send me an email if you have found one which is not already in this list.

Chapter 1

• p. 3, line -11: a convex subset should be a closed convex subset.
• p. 15, line 2: compact should be relatively compact.
• p. 22, line15: $\Sigma_{n=1}^{N}\frac{C_n^2+S_n^2}{2\pi n}$ should be $\Sigma_{n=1}^{N}\frac{C_n^2+S_n^2}{4\pi n}$.
Chapter 2

• p. 34, line -5: σ(s) should be σ(r+s).
• p. 35, line 7 of the proof of Corollary 2.16: the second \pi_n(s_1) should be \pi_n(s_2).
• p. 38, line 4: $\pi_n(a)$ should be $\pi_n(\mathbf{a})$.

Chapter 3

• p. 43, line 8: signature of X should be signature of x.
• p. 45, line 6 of the third paragraph: with respect to X should be with respect to x.
• p. 47, line11: finite $\frac{n+1}{p}$ variation should be finite $\frac{p}{n+1}$ variation.
• p. 50, after On the other hand, the equality should be

*
                   *
                              *.

• p. 50, line -3:  $X^D-X^{\tilde{D}}$ should be $\widehat{X}_{s,t}^D-\widehat{X}_{s,t}^{\tilde{D}}$.
• p. 55, line -4: $T^2(R^d)$ should be $T^{(2)}(R^d)$.

Chapter 4

• p. 64, line 14: $2Cn^{-\alpha}|t-s|$ should be  $2Cn^{-\alpha}|t-s|^{1+\alpha}$.
• p. 64, line -6: the r.h.s. of (4.4), $2^{1+\alpha}(\zeta(1+\alpha)-1)||h||_{Lip(\alpha)}|t-s|^{1+\alpha}$, should be $[1+2^{1+\alpha}(\zeta(1+\alpha)-1)]||h||_{Lip(\alpha)}|t-s|^{1+\alpha}$.
• p. 66, line -3: the r.h.s. of (4.6), $2^{\theta}(\zeta(\theta)-1)\omega(s,t)^{\theta}$, should be $[1+2^{\theta}(\zeta(\theta)-1)]\omega(s,t)^{\theta}$.
• p. 66, line -1: finer than should be the common refinement of.
• p. 71, line -6: $v_{1,k_n}$ should be $v_{n,k_n}$.
• p. 73, line -6: $||R_0(x,y)||\leq ||\alpha||_{Lip}||x-y||$ should be $||R_0(x,y)||\leq ||\alpha||_{Lip}||x-y||^{\gamma}$.


Many thanks to Gechun Liang.