A.2 Review of Concepts Related to Dynamical Systems 281 ·························································································· · · · · · · · Consider the stochastic process (A.2) on a nonempty open subset A of R n . Let x be a · · 1 linearly unstable rest point of f and t,+ be the projection of t 1 on E + in the direction of · · · E - . Assume that: · · · · · f is continuously differentiable and its derivative is Lipschitz continuous on a neighbor- · · · hood of x ; · j · · · { t }, j {1, 2} are stochastic processes adapted to filtration F t , i.e., for each time slot · · t N, t 1 and t 2 are random variables that are measurable with respect to F t , where F t · · · is the -algebra corresponding to the history of the system up to the end of period t; · · 1 1 2 < , · · E t+1 |F t = 0 almost surely (a.s), and lim sup t - E · - t+1 · · · 1 2 | F > 0 almost surely; lim inf t - E · - t t+1,+ · · 2 2 < almost surely; · · · t t1 · · · Then, lim t - q t = x with probability 0. · - · ´ Theorem 217: Brandi ere and Duflo (1996) A.2.2 Appendix to Chapter 8 In Chapter 8, we mentioned several assumptions (called [H1]­[H5]) under which