On a problem of approximation of Markov chains by a solution of a stochastic differential equation

机译：随机微分方程解的逼近马尔可夫链近似的问题

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Much scientific works has been done on the applications of the Brownian motion in such diverse areas as molecular and atomic physics, chemical kinetics, solid-state theory, stability of structures, population genetics, communications, and many other branches of the natural and social sciences and engineering. We shall refer below to some aspects concerning the approximation of Markov chains by a solution of a stochastic differential equation to determine the probability of extinction of a genotype. Thus, the Markovian nature of the problem will be pointed out.

机译：在这种不同地区的布朗运动的应用中，为分子和原子物理学，化学动力学，固态理论，结构稳定性，人口遗传，通信以及许多自然和社会科学分支机构的稳定性，已经完成了许多科学作品和工程。通过随机微分方程的解决方案，将以下几个方面提及关于马尔可夫链的近似，以确定基因型消灭的概率。因此，将指出问题的马尔可维夫性质。

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《International Conference on Chaotic Modeling, Simulation, and Applications》|2011年||共11页
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作者
Gabriel V. Orman;
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正文语种
中图分类 O415.5-532;
关键词
Brownian motion; stochastic differential equations; Markov chains; transition probabilities; binomial distribution;

机译：布朗运动;随机微分方程;马尔可夫链;过渡概率;二重传发行;

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1. Comparison of Markov Chain and Stochastic Differential Equation Population Models Under Higher-Order Moment Closure Approximations [J] . Amy J. Ekanayakea* Linda J. S. Allena Stochastic Analysis and Applications . 2010,第6期

机译：高阶矩闭合近似下的马尔可夫链和随机微分方程种群模型的比较
2. Comparison of Markov Chain and Stochastic Differential Equation Population Models Under Higher-Order Moment Closure Approximations [J] . AMY J. EKANAYAKE, LINDA J. S. ALLEN Stochastic Analysis and Applications . 2010,第6期

机译：高阶矩闭合近似下的马尔可夫链和随机微分方程种群模型的比较
3. Analytic approximation of the solutions of stochastic differential delay equations with Poisson jump and Markovian switching [J] . Yang H., Jiang F. Journal of applied mathematics . 2012,第Pta1期

机译：泊松跃迁和马尔可夫切换的随机微分时滞方程解的解析逼近
4. On a problem of approximation of Markov chains by a solution of a stochastic differential equation [C] . Gabriel V. Orman International Conference on Chaotic Modeling, Simulation, and Applications . 2011

机译：随机微分方程解的逼近马尔可夫链近似的问题
5. Wiener-Hopf Factorization for Time-inhomogeneous Markov Chains and Statistical Inference for Stochastic Partial Differential Equations [D] . Huang, Yicong. 2018

机译：随机偏微分方程的时源性马尔可夫链和随机偏微分方程的统计推断维纳 - HOPF分解
6. Multiscale Stochastic Reaction–Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations [O] . Hye-Won Kang, Radek Erban -1

机译：马尔可夫链模型与随机偏微分方程相结合的多尺度随机反应扩散算法
7. Solutions of Backward Stochastic Differential Equations on Markov Chains [O] . Cohen, Samuel N., Elliott, Robert J. 2008

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8. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. [R] . Trenchea, C. 2012

机译：基于高维随机偏微分方程解的跟踪统计量的有效数值逼近。

On a problem of approximation of Markov chains by a solution of a stochastic differential equation

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