In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application...In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application of our findings concerns P{sup_t∈|0,T|(X(t)+g(t))>u},as u→∞,for X a centered Gaussian process and g some measurable trend function.Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.展开更多
基金supported by Swiss National Science Foundation (Grant No. 200021166274)the National Science Centre (Poland) (Grant No. 2015/17/B/ST1/01102) (2016–2019)
文摘In this paper,we are concerned with the asymptotic behavior,as u→∞,of P{sup_t∈|0,T|X_u(t)>u},where X_u(t),t∈|0,T|,u>0 is a family of centered Gaussian processes with continuous trajectories.A key application of our findings concerns P{sup_t∈|0,T|(X(t)+g(t))>u},as u→∞,for X a centered Gaussian process and g some measurable trend function.Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.
