Acta Mathematicae Applicatae Sinica, English Series

In this paper, we investigate the asymptotic behavior for the finite- and infinite-time ruin probabilities of a nonstandard renewal model in which the claims are identically distributed but not necessarily independent. Under the assumptions that the identical distribution of the claims belongs to the class of extended regular variation (ERV) and that the tails of joint distributions of every two claims are negligible compared to the tails of their margins, we obtain the precise approximations for the finite- and infinite-time ruin probabilities.

In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a D-cone. A D-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.

The model of a kind of predator-parasite-pest system is built in this paper in which the parasite population is controlled by predator in such a way that it preys upon the pest individuals parasitized. A disgusty of predator for preying upon the pest individuals parasitized is introduced in the model to measure the intensity that the parasite population was controlled by the predator. The persistence and the stability are studied for this system mathematically. And the influence of the disgusty on the persistence of the system is also noticed in biology.

A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.

In this paper, we study the point process of state transitions in a regular Markov chain. Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution, the renewal distribution and the entering probability. As an application, using these formulas we derive the LS transform of the busy period for theM/M/∞ queue.

This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet.

Let n ≥ r, let π = (d 1, d 2, ..., d n ) be a non-increasing sequence of nonnegative integers and let K r+1 − e be the graph obtained from K r+1 by deleting one edge. If π has a realization G containing K r+1 − e as a subgraph, then π is said to be potentially K r+1 − e-graphic. In this paper, we give a characterization for a sequence π to be potentially K r+1 − e-graphic.

A matching is extendable in a graph G if G has a perfect matching containing it. A distance q matching is a matching such that the distance between any two distinct matching edges is at least q. In this paper, we prove that any distance 2k − 3 matching is extendable in a connected and locally (k − 1)-connected K1,k-free graph of even order. Furthermore, we also prove that any distance q matching M in an r-connected and locally (k − 1)-connected K1,k-free graph of even order is extendable provided that ∣M∣ is bounded by a function on r, k and q. Our results improve some results in [J. Graph Theory 93 (2020), 5–20].