Chapter 1 Edit
page 17 One reads:







A transition function has not been defined, but the definition could be guessed as the minimum requirements needed for the definition of $ P_n $ to make sense. See https://en.wikipedia.org/wiki/Markov_kernel
page 17 One reads





It should be $ P(dq) $ instead of $ P(dq') $ on the right hand side of the display.
page 18 One reads



Instead of $ q_{n+1} $ it should be $ q_{m+1} $.
page 19 one reads:


It should be a nonincreasing sequence instead.
page 26  27 One reads















It should be $\theta(t) \eta(t)  \int_s^t\theta(u)\, d \eta(u)$ those are two typos in the above pages
page 33 One reads

It should be by (3.13) instead of (3.12)
page 37  One reads:






But it should be $P(\sup \{x(t_2)  x(t_1) > \delta (...) \}$
Chapter 6 Edit
page 157  One reads: "One immediate application of Theorem 4.6.3 to the martingale problem is that the martingale problem is well posed (...)" As one goes back to chapter 4 there is no theorem on this entry only an exercise which does not seem to apply to the present case. The authors meant to say Theorem 6.4.3
page 161  One reads
But it should be


page 162  The super indices s are misplaced on the following lines
It should not be $\tau_{n1^s}$ but $\tau^s_{n1}$
page 163 one reads:

But it should be $\tau^n_1 = x + 1$ or $\tau^n_2 = x + 2$
page 163 one reads


But it should be $\tau^n_2 = \tau^n_1 + 1 \geq s+ 1$
page 163 One reads
But in light of the theorem 4.2.1 that we are using :
It should be $ 2d \exp \bigg(\frac{(\rho B \delta)^2}{2 Aa d \delta}\bigg) $
Chapter 12 Edit
page 288 one reads
instead of $ f: comp(X) \to comp(X) $ it should be $ F: comp(X) \to comp(X) $ or any other letter, since f is already taken and different functions should have different names.
page 293: One reads


Instead of a $ P $null set it should be a $ P_{s,x} $ null set
page 295: One reads




But instead of $ f(x(t+s))\,dt) $ it should be $ f(x(t+s))\,dt $
page 296  One reads

Instead of Theorem 12.4.3 it should be theorem 12.2.3
page 298  One reads



Instead of $ (q,s) \mapsto P^{\alpha(q)}_{x} $ it should be $ (q,s) \mapsto P^{\varphi(q)}_{x} $
page 299 One reads
Instead it should be "it suffices to show that the righthand side of (3.2) dominates the left"page 301: One reads

Instead of $ P^{s_1,\ldots, s_{n1},z}_s $ it should be $ P^{s_1,\ldots, s_{n1},z}_x $