# Asymptotic Methods in the Theory of Gaussian Processes and Fields

@inproceedings{Piterbarg1995AsymptoticMI, title={Asymptotic Methods in the Theory of Gaussian Processes and Fields}, author={Vladimir I. Piterbarg}, year={1995} }

Introduction The method of comparison The double sum method The method of moments Limit theorems for the number of high excursions and for maxima of Gaussian processes and fields References.

## 598 Citations

### Exact Asymptotic for the Tail of Maximum of Smooth Random Field Distribution

- Mathematics
- 2009

We obtain in this paper using the saddle point method the expression for the exact asymptotic for the tail of maximum of smooth (twice continuous differentiable) random field (process) distribution.

### On asymptotic constants in the theory of extremes for Gaussian processes

- Computer Science, Mathematics
- 2012

This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes, and resolves the long-standing problem of devising a reliable algorithm for estimating these constants.

### Almost sure asymptotics for extremes of non-stationary Gaussian random fields

- Mathematics
- 2014

In this paper, the authors prove an almost sure limit theorem for the maxima of non-stationary Gaussian random fields under some mild conditions related to the covariance functions of the Gaussian…

### On the Density Functions of Integrals of Gaussian Random Fields

- Mathematics, Computer ScienceAdvances in Applied Probability
- 2013

Close-form asymptotic bounds are provided for the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields and exact tail approximations of thedensity functions are derived.

### Some Asymptotic Results of Gaussian Random Fields with Varying Mean Functions and the Associated Processes

- Mathematics, Computer Science
- 2011

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This…

### Functional central limit theorem for the volume of excursion sets generated by associated random fields

- Mathematics
- 2011

### Extremal behavior of the heat random field

- Mathematics
- 2005

We study the exponential type inequalities for the distribution of the supremum of a random field that arises as the solution of the heat equation with a random initial condition that is a strictly…

### The almost sure limit theorem for the maxima and minima of strongly dependent Gaussian vector sequences

- Mathematics
- 2012

We derive the joint limiting distribution and the almost sure limit theorem for the maxima and minima for a strongly dependent stationary Gaussian vector sequence.

### The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited.

- Mathematics
- 2002

This paper deals with the problem of obtaining methods to compute the distribution of the maximum of a one-parameter stochastic process on a fixed interval, mainly in the Gaussian case. The main…