Methodology and Computing in Applied Probability

In this paper we obtain some “general” two-sided bounds for the delayed renewal function, in the sense that the bounds are valid for any arbitrary distributions of the inter-arrival times. Also, we give a sequence of monotone non-decreasing (non-...$\mathit{}$$\mathit{}$$\mathit{}$$\mathit{}$$\mathit{}$

We offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic ...

In this paper, we establish the complete f-moment convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of extended negatively dependent (END, for short) random variables under sub-linear expectations, which ...

This paper considers some asymptotics of value-at-risk (VaR) and conditional value-at-risk (CVaR) estimates in the cases of extended negatively dependent (END) and widely orthant dependent (WOD) sequences. The Bahadur representation and strong ...

A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high ...

This paper concerns the dynamics of a stochastic regime-switching four-species food chain model with distributed delays, Lévy jumps and harvesting in a polluted environment. First, under some basic assumptions, criterions about stochastic ...

In this paper, we study the optimal investment and proportional reinsurance problem for an insurer with short-selling and borrowing constraints under the expected value premium principle. The claim process follows a Brownian risk model with a ...

We consider a continuous-time branching random walk (BRW) on a one-dimensional lattice on which there is one center (the lattice point) of particle generation, called branching source. The generation of particles in the branching source is ...

The objective of this study is devoted to studying the equilibrium strategy of an unreliable M/M/1+1 retrial queue model, which contains two types of parallel customers and batch service provided by a standby server. Two kinds of customers in this ...

This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that ...

In the present we provide the definition of the new concept of the General Non-Homogeneous Markov System (G-NHMS) and establish the expected population structure of a NHMS in the various states. These results will be the basis to build on the new ...$\left(,,\mathrm{},,\right]$

The theory of linear recurrence sequences is applied to obtain an explicit formula for the ultimate ruin probability in a discrete-time risk process. It is assumed that the claims distribution is arbitrary but has finite support $\mathbf{\{}\mathbf{0}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{\dots }\mathbf{,}\mathit{m}\mathbf{+}\mathbf{1}\mathbf{\}}$, for ...$\mathit{}\mathbf{}\mathbf{}$

This paper considers a multidimensional risk model with cádlág investment return processes, in which there exists some dependence structure among claims and claim-arrival time. Specifically, if claims follow the subexponential distribution or the ...

The self-adjoint, positive Markov operator defined by the Pólya-Gamma Gibbs sampler (under a proper normal prior) is shown to be trace-class, which implies that all non-zero elements of its spectrum are eigenvalues. Consequently, the spectral gap ...$\mathrm{}_{}^{}$$_{}^{}\mathrm{}\mathrm{}$$_{}^{}$