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...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.展开更多
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 d...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.展开更多
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 process...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.展开更多
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 mode...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.展开更多
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-modul...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.展开更多
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 differen...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.展开更多
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 p...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.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(2020RC001)。
文摘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.
基金the National Natural Science Foundation of China (60674027, 60574007)Doctoral Foundation of Education Ministry of China (20050446001).
文摘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.
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China (10671182)Anhui Natural Science Foundation (090416225)+1 种基金Anhui Natural Science Foundation of Universities (KJ2010A037, KJ2010B026)Anhui Natural Science Foundation (10040606Q03)
文摘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.
文摘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.
基金Supported partly by Grand-in-Aid for Scientific Research (C)
文摘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.
