On the Stability of Stochastic Jump Kinetics
On the Stability of Stochastic Jump Kinetics
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论随机跳跃动力学的稳定性
DOI：
10.4236/am.2014.519300
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发表时间：
2012
影响因子：
1
通讯作者：
Stefan Engblom
中科院分区：
文献类型：
--
作者：
Stefan Engblom
出于缺乏一个合适的建设性框架，分析流行的随机模型的系统生物学，我们设计的条件，某些跳跃随机微分方程（SDES）的解的存在性和唯一性。从简单的例子中，我们发现合理的和明确的假设的驱动系数的ESTA表示是有意义的。所谓“合理”，我们的意思是，更强的假设一般不适用于具有实际意义的系统。特别是，我们反对传统的使用全球Lipschitz条件和某些常见的增长限制。最后，通过“显式”，我们想强调这样一个事实，即一旦模型固定，我们的假设中出现的各种常数都可以确定。我们展示了如何基本的长时间估计和一些限制结果的扰动，可以得出在这种情况下，这些可以与相应的估计确定性动力学形成对比。主要的复杂性是，自然的路径表示是由一个计数措施，强度依赖于非线性的状态。
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.