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

Roman Chertovskih; Evelina Shamarova

doi:10.1007/s11118-022-10015-y

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arXiv · 2002.11706

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

Roman Chertovskih·Evelina Shamarova

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Abstract

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.

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BibTeX RIS

Roman Chertovskih, Evelina Shamarova. 2022-06-20. Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression. https://doi.org/10.1007/s11118-022-10015-y

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