Methodology and Computing in Applied Probability最新文献

Based on the design and potential application of wind-solar storage intelligent power generation systems in engineering practice, this paper develops a novel reliability model of k-out-of-n: G mixed standby retrial system with failure dependency and J-vacation policy. The working components in the system have redundant dependencies. When any component of the system fails and the repairman is working or on vacation, the failed component goes into the retrial space. If the retrial space has no failed components, the idle repairman goes on vacation, which may last for up to J consecutive vacations, until at a minimum one failed component appears in the retrial space on a vacation return. Firstly, the performance indexes of the system under steady state are analyzed based on the Markov process theory. Secondly, an algorithm for modelling the failure process of the proposed model is developed through a Monte Carlo method, and numerical solutions for the reliability function and mean time to first failure (MTTFF) are presented. Then, some numerical examples are provided to demonstrate the influence of different parameters on the system reliability indexes. Finally, a system cost optimization model based on availability control is developed, and the optimal component configuration schemes for systems with no vacations and different maximum numbers of vacations J are compared and analyzed by genetic algorithm (GA).

Abstract

This paper investigates the optimal asset-liability management problems for two managers subject to relative performance concerns in the presence of stochastic inflation and stochastic volatility. The objective of the two managers is to maximize the expected utility of their relative terminal surplus with respect to that of their competitor. The problem of finding the optimal investment strategies for both managers is modeled as a non-zero-sum stochastic differential game. Both managers have access to a financial market consisting of a risk-free asset, a risky asset, and an inflation-linked index bond. The risky asset’s price process and uncontrollable random liabilities are not only affected by the inflation risk but also driven by a general class of stochastic volatility models embracing the constant elasticity of variance model, the family of state-of-the-art 4/2 models, and some path-dependent models. By adopting a backward stochastic differential equation (BSDE) approach to overcome the possibly non-Markovian setting, closed-form expressions for the equilibrium investment strategies and the corresponding value functions are derived under power and exponential utility preferences. Moreover, explicit solutions to some special cases of our model are provided. Finally, we perform numerical studies to illustrate the influence of relative performance concerns on the equilibrium strategies and draw some economic interpretations.

We consider coherent systems subject to random shocks that can damage a random number of components of a system. Based on the distribution of the number of failed components, we discuss three models, namely, (i) a shock can damage any number of components (including zero) with the same probability, (ii) each shock damages, at least, one component, and (iii) a shock can damage, at most, one component. Shocks arrival times are modeled using three important counting processes, namely, the Poisson generalized gamma process, the Poisson phase-type process and the renewal process with matrix Mittag-Leffler distributed inter-arrival times. For the defined shock models, we discuss relevant reliability properties of coherent systems. An optimal replacement policy for repairable systems is considered as an application of the proposed modeling.

Let (X_1,X_2,...) be the digits in the base-q expansion of a random variable X defined on [0, 1) where (qge 2) is an integer. For (n=1,2,...), we study the probability distribution (P_n) of the (scaled) remainder (T^n(X)=sum _{k=n+1}^infty X_k q^{n-k}): If X has an absolutely continuous CDF then (P_n) converges in the total variation metric to the Lebesgue measure (mu ) on the unit interval. Under weak smoothness conditions we establish first a coupling between X and a non-negative integer valued random variable N so that (T^N(X)) follows (mu ) and is independent of ((X_1,...,X_N)), and second exponentially fast convergence of (P_n) and its PDF (f_n). We discuss how many digits are needed and show examples of our results.

Abstract

In this paper, we consider a queueing inventory model with K service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (s, S) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.

We study the first exit time of a fractional Brownian motion with a drift from a parabolic domain. Actually, we explore three different regimes. In the first regime, the role of drift is negligible. In the second regime, the role of drift is dominating. The behavior of exit probability is the same as that of the crossing probability of a certain moving non-random boundary. In particular, the most interesting, intermediate regime, where all factors come into play, has been solved in this paper. Finally, numerical simulations are conducted, providing an approximate range for the asymptotic estimates to illustrate the practical implications and potential applications of our main results.

Let (Z(t)= exp left( sqrt{ 2} B_H(t)- left|t right|^{2H}right) , tin mathbb {R}) with (B_H(t),tin mathbb {R}) a standard fractional Brownian motion (fBm) with Hurst parameter (H in (0,1]) and define for x non-negative the Berman function

where the random variable R independent of Z has survival function (1/x,xgeqslant 1) and

In this paper we consider a general random field (rf) Z that is a spectral rf of some stationary max-stable rf X and derive the properties of the corresponding Berman functions. In particular, we show that Berman functions can be approximated by the corresponding discrete ones and derive interesting representations of those functions which are of interest for Monte Carlo simulations presented in this article.

The Hawkes process models have been recently become a popular tool for modeling and analysis of neural spike trains. In this article, motivated by neuronal spike trains study, we propose a novel multivariate generalized linear Hawkes process model, where covariates are included in the intensity function. We consider the problem of simultaneous variable selection and estimation for the multivariate generalized linear Hawkes process in the high-dimensional regime. Estimation of the intensity function of the high-dimensional point process is considered within a nonparametric framework, applying B-splines and the SCAD penalty for matters of sparsity. We apply the Doob-Kolmogorov inequality and the martingale central limit theory to establish the consistency and asymptotic normality of the resulting estimators. Finally, we illustrate the performance of our proposal through simulation and demonstrate its utility by applying it to the neuron spike train data set.

In this paper, the stochastic dynamics of a hybrid delay food chain model with harvesting and Lévy jumps in a polluted environment is studied by using stochastic analysis techniques. Under some basic assumptions, criterions about stochastic persistence in mean and extinction of each species are established, as well as global attractivity and the existence of optimal harvesting strategy (OHS) of the system. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the stochastic dynamics and OHS of the system are closely correlated with both time delays and environmental noises. Finally, some numerical simulations are introduced to illustrate the main results.

This paper examines the classical matching distribution arising in the “problem of coincidences”. We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed probability, and remaining non-matched items are allocated using simple random sampling without replacement. Our generalised matching distribution is a convolution of the classical matching distribution and the binomial distribution. We examine the properties of this latter distribution and show how its probability functions can be computed. We also show how to use the distribution for matching tests and inferences of matching ability.