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We then show that such moving average processes are equivalent to state space models with stochastic design components.
In fact, many authors have studied stochastic population models with stochastic noises, for example, Beddington and May [31], Liu and Bai [32, 33].
References [12, 13] and [14] considered predictors for δ in linear regression models with stochastic or non-stochastic linear constraints on the regression coefficients.
The study of insurance risk models with stochastic return on investments has attracted considerable attention recently; see for example Yin and Wen [8] and references therein.
Melnikov [3], Wang et al. [4] and Wei et al. [14] focused on risk models with stochastic premiums and when all capital of the insurer was invested in stock.
At the end of the paper, we would like to point out that one of the reviewers of this paper said 'Population models with stochastic noises may also be important and interesting.
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With the theory developed above, additional modeling efforts are needed to combine this model with stochastic features of linear statistical and landscape models for parameter estimation, genetic network construction and genotype-phenotype prediction in breeding populations.
Figure 7 Phase space portrait for the MSIRS endemic model with stochastic perturbations.
We consider nonlinear mixed-effects ODE model with stochastic approximation EM algorithm to overcome these difficulties.
We propose a state space mixed model with stochastic volatility for ordinal-response time series data.
In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force.
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