Displaying similar documents to “Long memory in economics : discussion and comments”

Lacunary Fractional brownian Motion

Marianne Clausel (2012)

ESAIM: Probability and Statistics

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In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Lacunary Fractional Brownian Motion

Marianne Clausel (2012)

ESAIM: Probability and Statistics

Similarity:

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Differential equations driven by fractional Brownian motion.

David Nualart, Aurel Rascanu (2002)

Collectanea Mathematica

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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.