Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density...

The noise level distribution owing to only a non-stationary working objective machine has been stochastically expressed by reflecting the temporal change of distribution parameters under a generalized regression model especially with aid of the vibration level observation. The proposed method has been applied to a noise evaluation of non-stationarily operated jigsaw. key words: non-stationary n...

This paper studies the subexponential asymptotics of the stationary distribution of an M/G/1-type Markov chain. We provide a sufficient condition for the subexponentiality of the stationary distribution. The sufficient condition requires only the subexponential integrated tail of level increments. On the other hand, the previous studies assume the subexponentiality of level increments themselve...

In this paper, we consider a stochastic Gilpin-Ayala population model with Markovian switching and white noise. All parameters are influenced by stochastic perturbations. We analyze the existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model, which g...

Asmussen (1987) proved a heavy-traffic limit theorem for the GI/G/1-type Markov chain. As a corollary, the theorem shows that in the heavy-traffic limit, the stationary distribution of the properly scaled level variable is geometric and independent of the phase variable. In this paper, the heavy-traffic asymptotics of the stationary distribution is proved under a weaker condition than Asmussen’...

The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures the degree of clustering of extremes in the multivariate process. In this paper, we construct nonparametric estimators of this function and prove their asym...

The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants t...

The results of Waldman (1982) on the Normal-Half Normal stochastic frontier model are generalized using the theory of the Dirac delta (Dirac, 1930), and distribution-free conditions are established to ensure a stationary point in the likelihood as the variance of the inefficiency distribution goes to zero. Stability of the stationary point and "wrong skew" results are derived or simulated for c...

Consideration is given to a discretetime queueing system with inverse discipline, service interruption and resumption, second-order geometrical demand arrival, arbitrary (discrete) distribution of demand length and finite storage. Each demand entering the queue has random volume besides its length. The total volume of the demands in the queue is limited by a certain number. Formulae for the sta...

Multivariate Markov chain models have previously been proposed in for studying dependent multiple categorical data sequences. For a given multivariate Markov chain model, an important problem is to study its joint stationary distribution. In this paper, we use two techniques to present some perturbation bounds for the joint stationary distribution vector of a multivariate Markov chain with s ca...