Iterated Random Functions
نویسندگان
چکیده
منابع مشابه
Iterated Random Functions
Let (X, d) be a complete separable metric space and (F n) n≥0 a sequence of i.i.d. random functions from X to X which are uniform Lipschitz, that is, L n = sup x =y d(F n (x), F n (y))/d(x, y) < ∞ a.s. Providing the mean contraction assumption E log + L 1 < 0 and E log + d(F 1 (x 0), x 0) < ∞ for some x 0 ∈ X, it is known (see [4]) that the forward iterations M x n = F n • ... • F 1 (x), n ≥ 0,...
متن کاملIterated Random Functions
A bstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a simple unifying idea: the iterates of rand...
متن کاملA Central Limit Theorem for Iterated Random Functions
A central limit theorem is established for additive functions of a Markov chain that can be constructed as an iterated random function. The result goes beyond earlier work by relaxing the continuity conditions imposed on the additive function, and by relaxing moment conditions related to the random function. It is illustrated by an application to a Markov chain related to fractals.
متن کاملImportance sampling of heavy-tailed iterated random functions
We consider a stochastic recurrence equation of the form Zn+1 = An+1Zn + Bn+1, where E[logA1] < 0, E[log B1] <∞ and {(An, Bn)}n∈N is an i.i.d. sequence of positive random vectors. The stationary distribution of this Markov chain can be represented as the distribution of the random variable Z , ∑∞ n=0 Bn+1 ∏n k=1 Ak. Such random variables can be found in the analysis of probabilistic algorithms ...
متن کاملIterated Random Walk
– The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using the method of moments. When the number of iterations n → ∞, a time-independent asymptotic density is obtained. It has a simple symmetric exponential form ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Review
سال: 1999
ISSN: 0036-1445,1095-7200
DOI: 10.1137/s0036144598338446