| EPSRC Reference: |
GR/R40746/01 |
| Title: |
Mixing Conditions and Central Limit Theorems |
| Principal Investigator: |
Veretennikov, Professor A |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Applied Mathematics |
| Organisation: |
University of Leeds |
| Scheme: |
Fast Stream |
| Starts: |
09 August 2001 |
Ends: |
08 April 2003 |
Value (£): |
62,065
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
The project concerns limit theorems and weak dependence conditions for Markov and stationary processes. We will establish conditions under which the rate of decrease of various mixing coefficients can be effectively estimated via basic properties of the process. One of the main goals is to fill the gap between a huge literature which uses bounds for mixing coefficients as assumptions and a small number of papers where such bounds are established under clear conditions.The methodology which we are going to apply includes quasi-Lyapunov functions, Harris's recurrent Markov chain method, the coupling method, factorization identities, spectral theory and positive operator theory and Poisson equations for Markov kernels.We expect to investigate a new version of the coupling method which may provide better constants in the bounds for convergence to equilibrium. We will investigate the hypothesis that best possible mixing bounds, generally, do not just depend on spectral properties of a process. Best decreasing exponential and polynomial rates will be studied. We expect to obtain new generalizations of the Central Limit Theorem for dependent random variable under weak mixing conditions. In turn, this may imply new bounds for Green's functions for elliptic differential operators and certain integral operators.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.leeds.ac.uk |