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Abstract Let X 1 , X 2 , ... be independent and identically distributed random variables with support on non-negative integers and X (n) (n ≥ 1) denote the corresponding sequence of discrete record values. In the present paper, we derive weak and strong limit results for the spacings of discrete record values X (n + m) − X (n) (n → ∞) and discuss generation algorithms of discrete records. [ABSTRACT FROM AUTHOR]

Abstract In Yano et al. (2009), limit theorems (so called, Feynman–Kac penalizations) for the one-dimensional recurrent symmetric α -stable process weighted and normalized by negative (killing) Feynman–Kac functionals with small potential are studied. In this paper, we deal with the same problem for negative potentials diverging at infinity. [ABSTRACT FROM AUTHOR]

Abstract In this short paper we find that the Sobolev inequality 1 p − 2 ∫ f p d μ 2 p − ∫ f 2 d μ ≤ C ∫ | ∇ f | 2 d μ (p ≥ 0) is equivalent to the exponential convergence of the Markov diffusion semigroup (P t) to the invariant measure μ , in some Φ -entropy. We provide the estimate of the exponential convergence in total variation and a bounded perturbation result under the Sobolev inequality. Finally in the one-dimensional case we get some two-sided estimates of the Sobolev constant by means of the generalized Hardy inequality. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. Several examples are also presented along with the theory. [ABSTRACT FROM AUTHOR]

Abstract Consider the processes { L t ; t ≥ 0 } and { λ t ; t ≥ 0 } associated with a marked Hawkes process and its conditional intensity. In the present paper, the integration by parts formulas for those processes are constructed, and applied to the study on the absolute continuity for their conditional laws. Moreover, the sensitivity formulas for those processes with respect to the parameters are given. [ABSTRACT FROM AUTHOR]

Abstract This paper develops the asymptotic properties of a recently proposed measure of inequality emphasizing the status of the poor relative to the rich. A simulation confirms the asymptotic results are applicable in practice. [ABSTRACT FROM AUTHOR]

We consider a Lévy risk process and a Sparre-Andersen risk process with Parisian ruin in the presence of a constant dividend barrier. We demonstrate that with few exceptions, ruin occurs with probability one. Subsequently, generalizations to certain dependent risk processes are discussed. Despite the mathematical nature of this paper, its goal is to convey some simple conclusions to the actuarial community. The reader may focus solely on the introduction and conclusion sections (Sections 1 and 5, respectively) as well as the numerical illustrations. [ABSTRACT FROM AUTHOR]