Mathematical and Stochastic Growth Models

Many statistical and mathematical models of growth are developed in the literature and effectively applied to various conditions in the existent world that involve many research problems in the different fields of applied statistics. Nevertheless, still, there is an equally large number of conditions, which have not yet been mathematically or statistically modeled, due to the complex situations or formed models are mathematically or statistically inflexible. The present study is based on mathematical and stochastic growth models. The specification of both the growth models is depicted. A detailed study of newly modified growth models is mentioned. This research will give substantial information on growth models, such as proposed modified exponential growth models and their specifications clearly motioned which gives scope for future research.

A tractable framework for analyzing a class of nonstationary Markov models

We consider a class of infinite‐horizon dynamic Markov economic models in which the parameters of utility function, production function, and transition equations change over time. In such models, the optimal value and decision functions are time‐inhomogeneous: they depend not only on state but also on time. We propose a quantitative framework, called extended function path (EFP), for calibrating, solving, simulating, and estimating such nonstationary Markov models. The EFP framework relies on the turnpike theorem which implies that the finite‐horizon solutions asymptotically converge to the infinite‐horizon solutions if the time horizon is sufficiently large. The EFP applications include unbalanced stochastic growth models, the entry into and exit from a monetary union, information news, anticipated policy regime switches, deterministic seasonals, among others. Examples of MATLAB code are provided.

Combinatorial Analysis of Growth Models for Series-Parallel Networks

We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths. Moreover, we introduce generalizations of these stochastic models by encoding the growth process of the networks via further important increasing tree structures.

COMPARATIVE DYNAMICS IN STOCHASTIC MODELS WITH RESPECT TO THEL∞–L∞DUALITY: A DIFFERENTIAL APPROACH

Many economic analyses are based on the property that the value of a commodity vector responds continuously to a change in economic environment. As is well known, however, many infinite-dimensional models, such as an infinite–time horizon stochastic growth model, lack this property. In the present paper, we investigate a stochastic growth model in which dual vectors lie in anL∞space. This result ensures that the value of a stock vector is jointly continuous with respect to the stock vector and its support price vector. The result is based on the differentiation method in Banach spaces that Yano [Journal of Mathematical Economics18 (1989), 169–185] develops for stochastic growth models.

The speed of extinction for some generalized jiřina processes

The speed of extinction for some generalized Jiřina processes {Xn} is discussed. We first discuss the geometric speed. Under some mild conditions, the results reveal that the sequence {cn}, where c does not equal the pseudo-drift parameter at x = 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such that Xn/cn, with a suitable constant cn, converges almost surely as n → ∞ to a proper, nondegenerate random variable. The main tools used in this paper are exponent martingales and stochastic growth models.