Publication

Simulation by circular embedding method of max-stable random fields

2009
Student Projects

Abstract

Theory of random fields or random processes is presented with an emphasis on the possible choices of correlation functions. Then two methods for generating Gaussian random fields in Rd are presented. The first method is a direct one but does not work for a too large number of locations. The second one is called the circular embedding method, works with large number of locations and had been introduced independently by Wood and Chan (1994) and Dietrich and Newsam (1993). It is exact in principle for correlation functions with compact support and an approximation method is given otherwise. Those methods have been implemented in R and validated by means of variogram comparisons. Finally Max-stable processes are introduced, the simulation procedure from Schlather's model is presented and max-stable process is simulated with help of the circular embedding method.

Official source

https://infoscience.epfl.ch/entities/publication/2fc3f40b-02dd-47d4-8151-c01dc8463f44

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2009
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2fc3f40b-02dd-47d4-8151-c01dc8463f44

About this result

Related concepts (32)

Random field

In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as ). That is, it is a function that takes on a random value at each point (or some other domain). It is also sometimes thought of as a synonym for a stochastic process with some restriction on its index set. That is, by modern definitions, a random field is a generalization of a stochastic process where the underlying parameter need no longer be real or integer valued "time" but can instead take values that are multidimensional vectors or points on some manifold.

Simulation

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.

Random walk

In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.

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Simulation by circular embedding method of max-stable random fields

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