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1.
This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.  相似文献   

2.
Stochastic differential delay equations of population dynamics   总被引:2,自引:0,他引:2  
In this paper we stochastically perturb the delay Lotka-Volterra model
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3.
In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples.  相似文献   

4.
Stochastic delay Lotka-Volterra model   总被引:1,自引:0,他引:1  
We reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay Lotka-Volterra model but will also make the solutions to be stochastically ultimately bounded. To reveal these interesting facts, we stochastically perturb the delay Lotka-Volterra model into the Itô form , and show that although the solution to the original delay equation may explode to infinity in a finite time, with probability one that of the associated stochastic delay equation does not. We also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix A.  相似文献   

5.
Consider a given system under regime switching whose solution grows exponentially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change significantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows exponentially become a new system whose solutions will grow at most polynomially. In other words, we reveal that the regime switching and the environmental noise will suppress the exponential growth.  相似文献   

6.
A stochastic model for internal HIV dynamics   总被引:1,自引:0,他引:1  
In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.  相似文献   

7.
This paper deals with the boundedness in probability and convergence for solutions of stochastic Liénard-type equations. Some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained. We also show that white noise can affect the boundedness of corresponding deterministic Liénard equations.  相似文献   

8.
The classical existence-and-uniqueness theorem of the solution to a stochastic differential delay equation (SDDE) requires the local Lipschitz condition and the linear growth condition (see e.g. [11], [12] and [20]). The numerical solutions under these conditions have also been discussed intensively (see e.g. [4], [10], [13], [16], [17], [18], [21], [22] and [24]). Recently, Mao and Rassias [14] and [15] established the generalized Khasminskii-type existence-and-uniqueness theorems for SDDEs, where the linear growth condition is no longer imposed. These generalized Khasminskii-type theorems cover a wide class of highly nonlinear SDDEs but these nonlinear SDDEs do not have explicit solutions, whence numerical solutions are required in practice. However, there is so far little numerical theory on SDDEs under these generalized Khasminskii-type conditions. The key aim of this paper is to close this gap.  相似文献   

9.
  总被引:1,自引:0,他引:1  
In this paper we introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.  相似文献   

10.
We define the compositionT° s,t of a Schwartz distributionT with a stochastic flow s,t generated by a stochastic differential equation. Then we establish a generalized Itô's formula for the composite processesT(t)° s,t andT(t)° s,t –1 , which describe a differential rule with respect to timet. The formula is then applied to two problems. One is the regularity of semigroups induced by the stochastic flow. The other is the existence and the continuity of the local time with respect to the spatial parameter, of a one dimensional stochastic flow.  相似文献   

11.
In this paper, first we consider model of exponential population growth, then we assume that the growth rate at time t is not completely definite and it depends on some random environment effects. For this case the stochastic exponential population growth model is introduced. Also we assume that the growth rate at time t depends on many different random environment effect, for this case the generalized stochastic exponential population growth model is introduced. The expectations and variances of solutions are obtained. For a case study, we consider the population growth of Iran and obtain the output of models for this data and predict the population individuals in each year.  相似文献   

12.
Stochastic Analysis of the Fractional Brownian Motion   总被引:20,自引:0,他引:20  
Since the fractional Brownian motion is not a semi-martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.  相似文献   

13.
钟丽华  柏灵 《应用数学》2012,25(3):506-514
本文考虑非线性随机扰动下的生态种群的问题.首先给出全局正解的存在性.其次,在合理的条件下讨论随机最终有界和随机持久问题,同时也给出解的渐近估计.  相似文献   

14.
我们将文献(Cipriano F,Cruzeiro A B.Navier-Stokes equation and diffusions on the group of homeomorphisms of the Torus[J].Commun.Math.Phys.,2007,275:255-269)推广到三维情形,即给出三维环面上的Navier-Stokes方程的随机变分准则.  相似文献   

15.
The main aim of this note is to improve some results obtained in the author's earlier paper (1999, J. Math. Anal. Appl.236, 350-369). From the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness.  相似文献   

16.
In this note we prove the exponential integrability of super-norms of general Itô's processes under certain assumptions, and then apply it to the diffusion processes determined by stochastic differential equations. In particular, a conjecture in [Y. Hu, Exponential integrability of diffusion processes, in: Contemp. Math., vol. 234, 1999, pp. 75-84] is solved.  相似文献   

17.
In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplacian on the circle is discussed in detail. Mathematics Subject Classification (2000): 60H15, 60G15  相似文献   

18.
This paper discusses a randomized nonautonomous logistic equation
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19.
This paper discusses a randomized non-autonomous logistic equation , where B(t) is a 1-dimensional standard Brownian motion. In [D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E[1/N(t)] has a unique positive T-periodic solution E[1/Np(t)] provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and . We show that this equation is stochastically permanent and the solution Np(t) is globally attractive provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and mint∈[0,T]a(t)>maxt∈[0,T]α2(t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded.  相似文献   

20.
The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.  相似文献   

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