TY - JOUR

T1 - Small deviations of sums of correlated stationary gaussian sequences

AU - Aurzada, F.

AU - Lifshits, M. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We consider the small deviation probabilities (SDP) in the uniform norm for sums of stationary Gaussian sequences. For the cases of constant boundaries and boundaries tending to zero, we obtain quite general results. For the case of the boundaries tending to infinity, we focus our attention on the discrete analogues of the fractional Brownian motion (FBM). It turns out that the lower bounds for the SDP can be transferred from the well-studied FBM case to the discrete time setting under the usual assumptions that imply weak convergence, while the transfer of the corresponding upper bounds necessarily requires a deeper knowledge of the spectral structure of the underlying stationary sequence.

AB - We consider the small deviation probabilities (SDP) in the uniform norm for sums of stationary Gaussian sequences. For the cases of constant boundaries and boundaries tending to zero, we obtain quite general results. For the case of the boundaries tending to infinity, we focus our attention on the discrete analogues of the fractional Brownian motion (FBM). It turns out that the lower bounds for the SDP can be transferred from the well-studied FBM case to the discrete time setting under the usual assumptions that imply weak convergence, while the transfer of the corresponding upper bounds necessarily requires a deeper knowledge of the spectral structure of the underlying stationary sequence.

KW - Fractional brownian motion

KW - Fractional gaussian noise

KW - Gaussian process

KW - Small deviation probability

KW - Stationary gaussian sequence

UR - http://www.scopus.com/inward/record.url?scp=85039147622&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T988356

DO - 10.1137/S0040585X97T988356

M3 - Article

AN - SCOPUS:85039147622

VL - 61

SP - 540

EP - 568

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

SN - 0040-585X

IS - 4

ER -