论文标题
用于多维向后SDE的解决方案的高斯型密度界限，并应用于基因表达
Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression
论文作者
论文摘要
我们在每个组件$ y^i_t $ y_t $ y_t $的密度上获得了上下高斯型界限，$ y_t $ $ y_t $ to多维非马克维亚向后SDE。我们的方法基于Nourdin-Viens公式，以及Wazewski定理的随机版本，内容涉及解决方案对颂歌的阳性。此外，我们将结果应用于随机基因表达。也就是说，我们估计基因调节网络中基因产生的蛋白质量的密度。
We obtain upper and lower Gaussian-type bounds on the density of each component $Y^i_t$ of the solution $Y_t$ to a multidimensional non-Markovian backward SDE. Our approach is based on the Nourdin-Viens formula and a stochastic version of Wazewski's theorem on the positivity of the components of a solution to an ODE. Furthermore, we apply our results to stochastic gene expression; namely, we estimate the density of the law of the amount of protein generated by a gene in a gene regulatory network.
