Corpus ID: 211507153

Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression

@article{Chertovskih2020GaussiantypeDB,
  title={Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression},
  author={Roman Chertovskih and Evelina Shamarova},
  journal={arXiv: Probability},
  year={2020}
}
  • Roman Chertovskih, Evelina Shamarova
  • Published 2020
  • Mathematics
  • arXiv: Probability
  • 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 backward SDE. Our approach is based on the Nourdin-Viens formula and the analysis of the associated semilinear parabolic PDE. 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. 

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