| Title |
Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk |
| Authors |
Kievinaitė, Dominyka ; Šiaulys, Jonas |
| DOI |
10.15559/18-VMSTA99 |
| Full Text |
|
| Is Part of |
Modern stochastics: theory and applications.. Vilnius; Kiev : VTeX. 2018, Vol. 5, no. 2, p. 129-143.. ISSN 2351-6054. eISSN 2351-6054 |
| Keywords [eng] |
Exponential bound ; supremum of sums ; tail probability ; risk model ; inhomogeneity ; ruin probability ; Lundberg's inequality |
| Abstract [eng] |
Let {ξ1,ξ2,…} be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability P(supn⩾0∑ni=1ξi>x) can be bounded above by ϱ1exp{−ϱ2x} with some positive constants ϱ1 and ϱ2 . A way to calculate these two constants is presented. The application of the derived bound is discussed and a Lundberg-type inequality is obtained for the ultimate ruin probability in the inhomogeneous renewal risk model satisfying the net profit condition on average. |
| Published |
Vilnius; Kiev : VTeX |
| Type |
Journal article |
| Language |
English |
| Publication date |
2018 |
