36 Pages

## Chapter 1 Edit

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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

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

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Instead of $q_{n+1}$ it should be $q_{m+1}$.

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It should be a non-increasing sequence instead.

page 26 - 27 One reads

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

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It should be by (3.13) instead of (3.12)

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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

But it should be

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page 162 - The super indices s are misplaced on the following lines

It should not be $\tau_{n-1^s}$ but $\tau^s_{n-1}$

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

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But it should be $\tau^n_2 = \tau^n_1 + 1 \geq s+ 1$

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

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.

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Instead of a $P$-null set it should be a $P_{s,x}$- null set

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

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Instead of Theorem 12.4.3 it should be theorem 12.2.3

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Instead of $(q,s) \mapsto P^{\alpha(q)}_{x}$ it should be $(q,s) \mapsto P^{\varphi(q)}_{x}$

Instead of $P^{s_1,\ldots, s_{n-1},z}_s$ it should be $P^{s_1,\ldots, s_{n-1},z}_x$