Markov Jump Processes in Estimating Sharing of Identity by Descent

Identity by descent(IBD)sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history.In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration.We adopt the structured coalescent theory and use a continuous-time Markov jump process{X(t),t≥0}to describe the genealogical process in such model.Then we apply Kolmogorov backward equation to calculate the distribution of coalescence time and develop a formula for estimating the IBD sharing.The simulation studies show that our method to estimate IBD sharing for this demographic model is robust and accurate.

THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES

Let X=(Omega,F,F-t,X(t),theta(t),P-x) be a jump Markov process with q-pair q(x)-q(x, A). In this paper, the equilibrium principle is established and equilibrium functions, energy, capacity and related problems is investigated in terms of the q-pair q(x)-q(x, A).

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems,assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.

STOPPED PROCESSES OF TEMPORALLY HOMOGENEOUS MARKOV JUMP PROCESSES

Let X=（X, （ω））(t≥0 be a jump process defined on a complete probability space （Ω, F, P）:

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

Markovian risk process

A Markovian risk process is considered in this paper, which is the generalization of the classical risk model. It is proper that a risk process with large claims is modelled as the Markovian risk model. In such a model, the occurrence of claims is described by a point process {N（t）}t≥0 with N（t） being the number of jumps during the interval （0, t] for a Markov jump process. The ruin probability ψ（u） of a company facing such a risk model is mainly studied. An integral equation satisfied by the ruin probability function ψ（u） is obtained and the bounds for the convergence rate of the ruin probability ψ（u） are given by using a generalized renewal technique developed in the paper.

不确定Markov跳跃线性系统的鲁棒跟踪与模型跟随

讨论一类带W iener过程的不确定M arkov跳跃线性系统的鲁棒跟踪和模型跟随问题.通过构造一组非线性鲁棒状态反馈跟踪控制器来跟踪给定的动态信号,该控制器确保系统当时间趋于无穷时是以扰动衰减系数鲁棒随机稳定的,且跟踪误差有界.最后给出了算例,说明所设计的鲁棒跟踪控制器具有较好的跟踪性能.

一类特殊空间下的齐次跳跃型Markov过程研究

对转移概率分布F(s,x;t,A)作出在可列状态空间I={0,1,2,…}条件下的特性进行了描述,进而得出关于齐次跳跃型Markov过程的4个具体结果,并加以证明.

非时齐跳跃Markov过程序列到扩散过程的弱收敛

本文给出了非时齐跳跃Markov过程序列弱收敛于非时齐扩散过程的一般性定理。利用这一定理,证明了非负非时齐跳跃Markov过程序列弱收敛于Brownian Excursion和经验分布过程弱收敛于Bown桥。

一类带Markov过程的Ito型随机系统的H_∞分析

研究一类带Markov跳过程的Ito型随机系统的H_∞分析问题。得到了随机系统稳定的充要条件,在给定干扰抑制水平γ的前提下,得到了随机γ-稳定的一个充要条件,并且此结果具有一定的广泛性。

Study on the model of an insurer's solvency ratio in Markov-modulated Brownian markets

In this paper the insurer＇s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer＇s solvency ratio is characterized by a Markov-modulated dynamics. By Girsanov＇s theorem and the option pricing formula, the expected present value of shareholders＇ terminal payoff is provided.

On the Stability of Stochastic Jump Kinetics

Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs). Working from simple examples we find reasonable and explicit assumptions on the driving coefficients for the SDE representation to make sense. By “reasonable” we mean that stronger assumptions generally do not hold for systems of practical interest. In particular, we argue against the traditional use of global Lipschitz conditions and certain common growth restrictions. By “explicit”, finally, we like to highlight the fact that the various constants occurring among our assumptions all can be determined once the model is fixed. We show how basic long time estimates and some limit results for perturbations can be derived in this setting such that these can be contrasted with the corresponding estimates from deterministic dynamics. The main complication is that the natural path-wise representation is generated by a counting measure with an intensity that depends nonlinearly on the state.

On Exit Time from Balls of Jump-type Symmetric Markov Processes

We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.

马氏风险过程

研究了一般马氏风险过程,它是经典风险过程的拓广.具有大额索赔的风险过程用此马氏风险模型来描述是适合的.在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数.主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界.

马氏环境下带扰动的Cox相关的风险模型破产概率的上界估计

本文讨论马氏环境下带随机扰动的保单数量过程与索赔次数过程Cox相关的风险模型.利用鞅方 法,给出了该风险模型的破产概率的指数上界.

一般状态空间跳过程不变测度的存在性和唯一性

本文利用一般状态空间马氏链关于不变测度的有关结果和跳过程的性质 。

石油价格跳跃下期货价格动态模型及实证分析

引入跳扩散过程描述石油价格的变化,在风险溢酬一定的假定下,推导出石油期货价格的动态变化模型和定价模型.通过石油期货价格数据对石油价格模型进行实证检验,发现石油价格具有两个显著特征:1)价格有明显的跳跃和均值回复特征,2)投资者对石油价格随机波动和跳跃风险要求正的风险溢酬.本文的另还利用两个期货价格序列对石油价格模型进行实证分析,它们可以用来确定风险溢酬参数,并用来分析石油价格的时间序列特征.

Q过程唯一性的实用判别准则（英文）

首先简要介绍自1977年左右开始的寻找连续时间马尔可夫跳过程实用的唯一性充分条件的故事.对于一般状态空间的一般性结果是1985年得到的.为展示这些充分条件的精确性,于1991年找到非唯一性的对偶判别准则.本文主要限于离散空间(此时的跳过程也称为Q过程或马尔可夫链).在这种情况下,我们将在文末证明上述充分条件也是必要的.我们还将举例说明不论对于唯一性或非唯一性,我们的充分条件不仅强有力,而且精确.

基于标值点过程改进的遥感道路提取新算法

研究了标值点过程的道路提取算法,针对传统数据模型提取道路不够准确的缺点,改进了数据模型。提出了基于边缘检测的生灭转移核,避免了传统的生灭过程搜索的盲目性,大大加快了算法的收敛速度。针对传统转移核容易破坏线段的连接性的缺点,定义了多种新型的RJMCMC转移核,重新设计了基于邻域的生灭转移核及线段参数转移核。仿真结果表明,改进算法大大提高了收敛速度,并且提取的道路网络更准确,更连续。

基于局部结构约束标识点过程的遥感影像道路提取

针对道路提取方法存在的漏提、误提等问题,提出一种基于局部结构约束的线段标识点过程提取算法。将道路网视作道路段集合,以随机点过程定义位置,以线段为标识定义几何结构,根据道路局部特征构建自适应的约束模型,结合道路的光谱同质性和异质性建立光谱测度模型,在贝叶斯理论构架下,综合上述模型和参数分布建立后验概率模型,设计可逆跳变马尔可夫链蒙特卡洛(RJMCMC)算法模拟采样,并为加快收敛速率设计高效的RJMCMC转移核,以最大化后验概率为准则,获取最优道路网。采用全色遥感影像进行实验、缓冲区评价方法进行定性和定量分析,计算得出道路提取的精准率和完整率分别能达到52%和98%以上,验证所提算法能准确有效地提取出道路网络。