36 Pages

## Chapter 3 - Feller Processes Edit

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one should be aware that to make exercise 3.2, it is important to use (3.2) and (3.3). see discussion in

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instead of $\mathbb{E}^x f(L(0)) g(X(\tau)) = \lim_{t \downarrow 0}\lim_{n\to \infty} \mathbb{E}^x f(X(\tau_n)) g (X(\tau_n + t))$ it should be $\mathbb{E}^x [f(L(0)) g(X(\tau))] = \lim_{t \downarrow 0}\lim_{n\to \infty} \mathbb{E}^x [f(X(\tau_n)) g (X(\tau_n + t))]$

## Appendix A.7 Discrete Time Martingales Edit

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Instead of $\mathbb{E} (\vert X_\alpha\vert , \vert X_\alpha \vert \geq N)\ \leq \frac{\mathbb{E}X^2_\alpha}{N}$ shouldn't it be $\mathbb{E} (\vert X_\alpha\vert , \vert X_\alpha \vert \geq N)\ \leq \frac{\mathbb{E}X^2_\alpha}{N^2}$