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Chapter 1 Edit

page 17 One reads:

SV clarification

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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

page 17 One reads

SV typo

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

page 18 One reads

SV typo1

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

page 19 one reads:
Varadhan typo3

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It should be a non-increasing sequence instead.

page 26 - 27 One reads

SV typo01

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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

page 33 One reads

SV typo02

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

page 37 - One reads:

SV tyyyy

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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

page 161 - One reads

Varadhan typo

But it should be

Varadhan typo1

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

Typo Stroock varadhan2

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

page 163 one reads:

Typo Stroock varadhan3

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

page 163 one reads

Typo Stroock varadhan4

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

page 163 One reads

Typo Stroock varadhan5

But in light of the theorem 4.2.1 that we are using :

Typo Stroock varadhan6

It should be $ 2d \exp \bigg(\frac{(\rho- B \delta)^2}{2 Aa d \delta}\bigg) $

Chapter 12 Edit

page 288 one reads

SV typo0

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

SV typo0.5

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

page 295: One reads

SV typo1-0

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

page 296 - One reads

SV typo0.6

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Instead of Theorem 12.4.3 it should be theorem 12.2.3

page 298 - One reads

SV typo2

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

page 299 One reads

SV typo10

Instead it should be "it suffices to show that the right-hand side of (3.2) dominates the left"page 301: One reads

SV typo review7

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