In the paper Existence de processus Markoviens pour des systèmes infinis de particules by Cocozza, C. and Kipnis, C. (Ann. lnst. H. Poincaré, Sect. B, 13, 239-257, 1977), one reads (pg 249)
While $A^{x_1,\ldots,x_k}_{t_1,\ldots,t_k}$ is defined in page 248 by:
The way it is written it is not true that $F_\epsilon \subset \big(A^{x_1,\ldots,x_k}_{t_1,\ldots,t_k}\big)^c$ however, from the computation of $P(t_i - \epsilon_{p,i}<T^{x_i}_p< t_i + \epsilon_{p,i})$ one is lead to believe that there is a typo in the definition of $F_\epsilon$ and that, instead of what is there, one should have $$F_\epsilon = \bigg[\bigcap_{i = 1}^k \bigcap_p (t_i - \epsilon_{p,i} <T^{x_i}_p < t_i + \epsilon_{p,i} ) \bigg] $$
Is this the case?
second typo: instead of $$P_n(N^{x_i}_{t_i + \epsilon_{p,i}}\geq 1) \leq \Bbb{E}_{P_n} (N^{x_i}_{t_i + \epsilon_{p,i}} - N^{x_i}_{t_i - \epsilon_{p,i}}) $$
shouldn't it be: $$P_n(N^{x_i}_{t_i - \epsilon_{p,i},t_i + \epsilon_{p,i}}\geq 1) \leq \Bbb{E}_{P_n} (N^{x_i}_{t_i + \epsilon_{p,i}} - N^{x_i}_{t_i - \epsilon_{p,i}}) $$
third typo: One reads
Here, instead of "il existe une fonction $F_\epsilon$ ($\ldots$)" shouldn't it be "il existe une fonction $f_\epsilon$ ($\ldots$)"?
