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Identification of the Multivariate Fractional Brownian Motion
Self similarity Multivariate process Long-range dependence Discrete variations Parametric estimation
2011/3/21
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p...
Fractional Brownian Motion and the Markov Property
Gaussian processes Markov Processes Numerical Approximation Ergodic Theorem
2009/5/8
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to:
1. A...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
heat equation white noise stochastic partial differential equations
2009/4/29
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...