http://www.hektor.umcs.lublin.pl/~komorow/mydoc/E2.pdf

Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. The Central Limit Theorem for random dynamical systems is established.

/pdf/the-central-limit-theorem-for-random-dynamical-systems-1pvwt4urvl.pdf

The Central Limit Theorem for Random Dynamical Systems

We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We prove the existence of an exponentially attractive invariant measure and the strong law of large numbers.

/pdf/law-of-large-numbers-for-random-dynamical-systems-1qvw4opbla.pdf

Law of Large Numbers for Random Dynamical Systems

We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of large numbers.

Law Of Large Numbers For Random Dynamical Systems

By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations.

https://www.aimsciences.org/article/exportPdf?id=247137af-5c6d-4cc3-905c-2fe5a2e6d381

Limit theorems for additive functionals of path-dependent SDEs

We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.

Anna Walczuk

Papers

Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric