Almost sure invariance principle for random piecewise expanding maps
نویسندگان
چکیده
منابع مشابه
Almost Sure Invariance Principle for Random Piecewise Expanding Maps
The objective of this note is to prove the almost sure invariance principle (ASIP) for a large class of random dynamical systems. The random dynamics is driven by an invertiblemeasure preserving transformation σ of (Ω,F ,P) called the base transformation. Trajectories in the phase space X are formed by concatenations f ω := fσn−1ω ◦ · · · ◦ fσω ◦ fω of maps from a family of maps fω : X → X, ω ∈...
متن کاملAn almost sure invariance principle for random walks in a space-time random environment
We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments wh...
متن کاملAlmost Sure Invariance Principle for Continuous- Space Random Walk in Dynamic Random Environ- ment
We consider a random walk on R in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit theorem to hold.
متن کاملAlmost Sure Invariance Principle for Nonuniformly Hyperbolic Systems
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon. Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, a...
متن کاملAn almost sure invariance principle for the range of planar random walks
For a symmetric random walk in Z2 with 2 + δ moments, we represent |R(n)|, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each k ≥ 1 (log n) 1 n |R(n)| + k ∑ j=1 (−1)( 1 2π log n + cX)−jγj,n → 0, a.s. where Wt is a Brownian motion, W (n) t = Wnt/ √ n, γj,n is the renormalized intersection ...
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: Nonlinearity
سال: 2018
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aaaf4b