The exponential moment tail of inhomogeneous renewal process

Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk

“…The results of the present paper are complementary to those obtained by Albrecher et al [1], Ambagaspitiya [2], Bernackaitė and Šiaulys [5,6], Castañer et al [7], Cojocaru [9], Constantinescu et al [10], Czarna and Palmowski [11], Damarackas and Šiaulys [12], Danilenko et al [13], Grigutis et al [17,18], Jordanova and Stehlík [20], Mishura et al [24], Rȃducan et al [26][27][28], Ragulina [29], Zhang et al [33], Zhang et al [34] and other authors who dealt with different inhomogeneous risk models.…”

“…Ee yξi n , by the inequality of arithmetic and geometric means. Equality (5) and inequalities (7), (8) imply that…”

A Lundberg-type inequality for an inhomogeneous renewal risk model

“…In [17], the authors consider the model where the interarrival times are identically distributed and have a particular distribution, whereas the claims are differently distributed with distributions belonging to a particular class. Bernackaitė and Šiaulys [4] deal with an inhomogeneous renewal risk model where the r.v.s {θ 1 , θ 2 , . .…”