scholarly journals Quadratic functionals and small ball probabilities for the $m$-fold integrated Brownian motion

2003 ◽  
Vol 31 (2) ◽  
pp. 1052-1077 ◽  
Author(s):  
Xia Chen
Keyword(s):  
Brownian Motion ◽  
Small Ball ◽  
Small Ball Probabilities ◽  
Quadratic Functionals

scholarly journals Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes

2020 ◽  
pp. 2050049
Author(s):  
Alexander I. Nazarov
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Gaussian Processes ◽  
Spectral Asymptotics ◽  
Eigenvalue Asymptotics ◽  
Small Ball ◽  
Small Ball Probabilities ◽  
Spectral Problems

We study spectral problems for integro-differential equations arising in the theory of Gaussian processes similar to the fractional Brownian motion. We generalize the method of Chigansky–Kleptsyna and obtain the two-term eigenvalue asymptotics for such equations. Application to the small ball probabilities in [Formula: see text]-norm is given.

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