Displaying similar documents to “Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations”

Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations

Renaud Marty (2005)

ESAIM: Probability and Statistics

Similarity:

We consider a differential equation with a random rapidly varying coefficient. The random coefficient is a gaussian process with slowly decaying correlations and compete with a periodic component. In the asymptotic framework corresponding to the separation of scales present in the problem, we prove that the solution of the differential equation converges in distribution to the solution of a stochastic differential equation driven by a classical brownian motion in some cases, by a fractional...

Random paths with bounded local time

Itai Benjamini, Nathanaël Berestycki (2010)

Journal of the European Mathematical Society

Similarity:

We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show...

Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of ( N , d ) -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the...