scholarly journals Estimation of the density of a determinantal process

10.5802/cml.1 ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 3-23 ◽  
Author(s):  
Yannick Baraud
Keyword(s):  
Determinantal Process

Random Walk in Random Scenery

2019 ◽  
pp. 382-404
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Random Walk ◽  
Central Limit ◽  
Functional Form ◽  
Stationary Sequence ◽  
Limit Behavior ◽  
Partial Sums ◽  
Determinantal Process ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
Random Scenery

In this chapter we investigate the question of central limit behavior and its functional form for the partial sums associated with a centered L2-stationary sequence of real-valued random variables (usually called the random scenery) sampled by a recurrent one-dimensional strongly aperiodic random walk. This question is handled under various conditions dependent on the random scenery. In particular, we assume that the random scenery either satisfies an asymptotic negative dependence condition, or is a function of a determinantal process and a Gaussian sequence, or satisfies a mild projective criterion. We first show that study of central limit behavior for such random walks in random scenery can be handled with results related to linear statistics developed in Chapter 12, provided the random walk has good properties. We then look extensively at the properties of a recurrent one-dimensional strongly aperiodic random walk. The functional form of the central limit theorem is also investigated.

scholarly journals Elliptic determinantal process of type A

2014 ◽  
Vol 162 (3-4) ◽  
pp. 637-677 ◽  
Author(s):  
Makoto Katori
Keyword(s):  
Type A ◽  
Determinantal Process
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