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131.
Ion Grama Ronan Lauvergnat Émile Le Page 《Stochastic Processes and their Applications》2019,129(7):2485-2527
Let be a branching process in a random environment defined by a Markov chain with values in a finite state space . Let be the probability law generated by the trajectories of starting at We study the asymptotic behaviour of the joint survival probability , as in the critical and strongly, intermediate and weakly subcritical cases. 相似文献
132.
Let be the first return time to of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, for an explicit constant . Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton. 相似文献
133.
134.
The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence. 相似文献
135.
The extinction phenomenon induced by multiplicative non-Gaussian Levy noise in a tumor growth model with immune response is discussed. Under the influence of the stochastic immune rate, the model is analyzed in terms of a stochastic differential equation with multiplicative noise. By means of the theory of the infinitesimal generator of Hunt processes, the escape probability, which is used to measure the noise-induced extinction probability of tumor cells, is explicitly expressed as a function of initial tumor cell density, stability index and noise intensity. Based on the numerical calculations, it is found that for different initial densities of tumor cells, noise parameters play opposite roles on the escape probability. The optimally selected values of the multiplicative noise intensity and the stability index are found to maximize the escape probability. 相似文献
136.
In this paper, we establish uniform-in-bandwidth limit laws of the logarithm for nonparametric Inverse Probability of Censoring
Weighted (I.P.C.W.) estimators of the multivariate regression function under random censorship. A similar result is deduced
for estimators of the conditional distribution function. The uniform-in-bandwidth consistency for estimators of the conditional
density and the conditional hazard rate functions are also derived from our main result. Moreover, the logarithm laws we establish
are shown to yield almost sure simultaneous asymptotic confidence bands for the functions we consider. Examples of confidence
bands obtained from simulated data are displayed.
相似文献
137.
138.
考虑了带二元连续变利息力的Sparre Andersen风险模型.研究了积累值盈余过程的表达式与性质;在利率递增环境下,利用推广后的调节系数方程组与递归技术推导了最终破产概率的上界,结论表明得到的破产概率上界是更为一般的Lundberg指数上界. 相似文献
139.
Estimation of rating classes and default probabilities in credit risk models with dependencies
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Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
140.
Mingzhong Li Chenwei Liu Chen Liang Jibin Li 《Journal of Dispersion Science and Technology》2014,35(3):397-402
In order to increase the present understanding of bimodal emulsion drop size distributions, systematic series of experiments have been carried out to investigate the effects of formulation variables on bimodal drop size distributions, and probability distribution functions were proposed to analyze the distribution. The results show that, the span of the drop size and Sauter mean diameter become larger when the dispersed phase volume fraction becomes higher and rotor speed becomes lower; the Frechet function represents the experimental data satisfactorily. The prediction model of Sauter mean diameter established by combining the prediction theory of the maximum stable drop diameter and experimental analysis results can fit the experimental data well. 相似文献