Multidimensional diffusion Processes

Chapter 1
page 17 One reads: -

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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

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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 -

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

page 19 one reads:

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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

page 33 One reads

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

page 37 - One reads:

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But it should be $P(\sup \{|x(t_2) - x(t_1)| > \delta (...) \}$

Chapter 6
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

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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 $\tau^s_{n-1}$

page 163 one reads:

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

page 163 one reads

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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
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 -

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

page 295: One reads -

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

page 296 - One reads

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Instead of Theorem 12.4.3 it should be theorem 12.2.3

page 298 - One reads

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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

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

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