The Linear Birth And Death Process With Binomially Distributed Catastrophes

The linear birth and death processes with binomially distributed catastrophesare an important model of Markov process. As it’s biologically relevant, it has greatpractical significance. The thesis is devoted to the studies on the linear birth anddeath processes with binomially distributed catastrophes, mainly include stochasticmonotonicity, duality, mean extinction time, extinction probability and the domainof attraction of the quasi-stationary distribution.In the first chapter, we introduce the background of the linear birth and deathprocesses with binomially distributed catastrophes.In the second chapter, firstly, we introduce our model, then we pay attentionto its stochastic monotonicity and duality.In the third chapter, we use a easier and more intuitive method to prove thethe necessary and sufcient conditions for certain extinction. At the same time, weobtain the the sufcient condition for E_iT₀<∞.In the fourth chapter§we obtain the lower bound for the decay parameter usingcomparative method.In the fifth chapter, we obtain the domain of attraction of the quasi-stationarydistribution for the linear birth and death processes with binomial distribution.In the sixth chapter, we devote to studying another important model（b_i=b, d_i=id） for birth and death processes with binomial distributed catastrophesusing the same thought to the former five chapters, and we obtain a series of similarresults.