This chapter is organized as follows. In Sect. 8.2, generalized renewal processes
constructed from random sequences are studied and a number of results are proved on the …

We introduce the notions of asymptotic quasi-inverse functions and asymptotic inverse
functions as weaker versions of (quasi-) inverse functions, and study their main properties …

In this paper we study the as asymptotic behaviour of the solution of the stochastic dfferential
equation dX (t)= g (X (t)) dt+ σ (X (t)) dW (t), X (0)= b> 0, where g and σ are positive …

Time-changed spectrally positive Levy processes started from infinity Page 1 Bernoulli 27(2), 2021,
1291–1318 https://doi.org/10.3150/20-BEJ1274 Time-changed spectrally positive Lévy processes …

In this paper we investigate the connection between the asymptotic relations of
subordination and the negligence with the generalized inverse function in the class of all …

We continue to study properties of functions which are asymptotic (quasi-) inverse for PRV
and POV functions. The equivalence of all quasi-inverses for POV functions is proved. Under …

This is a survey of the authors' results on the properties and applications of some subclasses
of (so-called) O-regularly varying (ORV) functions. In particular, factorization and uniform …

A characterization of normalizing functions connected with the limiting behavior of ratios of
asymptotic quasi-inverse functions is discussed. For nondecreasing functions, conditions …

Avakumović-Karamata functions f are generalized regularly varying functions (so--called
ORV functions) such that f*(λ)= limsup x→∞ f (λx)/f (x) is finite for all λ> 0. In this paper, we …

In this paper, we investigate the as asymptotic behavior of the solution of the stochastic
differential equation d X (t)= g (X (t)) dt+ σ (X (t)) dW (t), X (0)≢ 1, where g (·) and σ (·) are …