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math.PR2018
Mixed fractional Brownian motion: a spectral take
P. Chigansky, M. Kleptsyna, D. Marushkevych
This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its…
math.PR2018
Exact spectral asymptotics of fractional processes
P. Chigansky, M. Kleptsyna, D. Marushkevych
Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do, are usually solved by reduction to the ge…
math.PR2015
Gärtner-Ellis condition for squared asymptotically stationary Gaussian processes
Marina Kleptsyna, Alain Le Breton, Bernard Ycart
The Gärtner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed i…