Göran Högnäs and Brita Jung ANALYSIS OF A STOCHASTIC DIFFERENCE EQUATION : EXIT TIMES AND INVARIANT DISTRIBUTIONS
نویسندگان
چکیده
The mean return time of a discrete Markov chain to a point x is the reciprocal of the invariant probability π(x). We revisit this classical theme to investigate certain exit times for stochastic difference equations of autoregressive type. More specifically, we will discuss the asymptotics, as ε→ 0, of the first time τ that the n-dimensional process Yt = f(Yt−1) + εξt, t = 1, 2, . . . (where ξ1, ξ2, . . . is a sequence of i.i.d. random n-vectors) leaves a given neighborhood of the fixed point of the contraction f .
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