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2013
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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.spa.2013.06.007
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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_28B3A7E8CADC7
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E. Hashorva et al., « On the supremum of gamma-reflected processes with fractional Brownian motion as input », Serveur académique Lausannois, ID : 10.1016/j.spa.2013.06.007
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Let {X-H(t), t >= 0} be a fractional Brownian motion with Hurst index H is an element of (0, 1] and define a gamma-reflected process W-gamma(t) = X-H(t) - ct - gamma inf(s is an element of[0,t])(X-H(s) - cs), t >= 0 with c > 0, gamma is an element of [0, 1] two given constants. In this paper we establish the exact tail asymptotic behaviour of M-gamma(T) = sup(t is an element of[0,T]) W-gamma(t) for any T is an element of (0, infinity]. Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields.