论文标题
随机切换进化方程
Randomly switching evolution equations
论文作者
论文摘要
我们提出了对随机进化的调查，其中$ l^1 $中的进化方程家族是由连续时间马尔可夫过程驱动的。这些是在可集成函数空间上所谓的分段确定性马尔可夫过程（PDMP）的示例。我们在此类过程的第一刻和（任何顺序）的相关性中得出方程。我们还详细介绍了过程的平均值并描述其行为。结果通过一些简单但通用的生物学实例来说明，其特征是不同类型的分叉类型。
We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the space of integrable functions. We derive equations for the first moment and correlations (of any order) of such processes. We also introduce the mean of the process at large time and describe its behaviour. The results are illustrated by some simple, yet generic, biological examples characterized by different one-parameter types of bifurcations.
