Nonconventional limit theorems in discrete and continuous time via martingales
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Publication:2447337
DOI10.1214/12-AOP796zbMath1304.60041arXiv1012.2223MaRDI QIDQ2447337
Yuri Kifer, Srinivasa R. S. Varadhan
Publication date: 25 April 2014
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1012.2223
Markov processesmixinglimit theoremsmartingale approximationhyperbolic diffeomorphismpolynomial ergodic theorems
Gaussian processes (60G15) Martingales with discrete parameter (60G42) Functional limit theorems; invariance principles (60F17) Dynamical systems with hyperbolic behavior (37D99)
Related Items (24)
Berry-Esseen type estimates for nonconventional sums ⋮ Nonlinear large deviations ⋮ Some open problems on multiple ergodic averages ⋮ A nonconventional invariance principle for random fields ⋮ Stein's method for nonconventional sums ⋮ Nonconventional Poisson limit theorems ⋮ Nonconventional moderate deviations theorems and exponential concentration inequalities ⋮ A local limit theorem for a number of multiple recurrences generated by some mixing processes with applications to Young towers ⋮ Large deviations, moment estimates and almost sure invariance principles for skew products with mixing base maps and expanding-on-average fibers ⋮ Boundary complexity and surface entropy of 2-multiplicative integer systems on Nd ⋮ A strong invariance principle for nonconventional sums ⋮ Strong diffusion approximation in averaging and value computation in Dynkin's games ⋮ Large deviation principle of multiplicative Ising models on Markov-Cayley trees ⋮ Scale-free graphs with many edges ⋮ Nonconventional averages along arithmetic progressions and lattice spin systems ⋮ Nonconventional limit theorems in averaging ⋮ Strong approximations for nonconventional sums and almost sure limit theorems ⋮ Nonconventional large deviations theorems ⋮ Poisson and compound Poisson approximations in conventional and nonconventional setups ⋮ A nonconventional local limit theorem ⋮ Tails of polynomials of random variables and stable limits for nonconventional sums ⋮ Averaging principle and normal deviations for multiscale stochastic systems ⋮ A functional CLT for nonconventional polynomial arrays ⋮ An introduction to large deviations for random graphs
Cites Work
- From discrete- to continuous-time ergodic theorems
- Weakly mixing PET
- Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C 2 - Transformations
- Equilibrium states and the ergodic theory of Anosov diffeomorphisms
- Nonconventional limit theorems
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