Borel summation of the small time expansion of some SDE's driven by Gaussian white noise

Sergio Albeverio; Boubaker Smii

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arXiv · 1810.13158

Borel summation of the small time expansion of some SDE's driven by Gaussian white noise

Sergio Albeverio·Boubaker Smii

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Abstract

We consider stochastic differential equations driven by Gaussian white noise on $\R^d$. % We provide applications to models for financial %markets. Particular attention is given to the kernel $p_t,\,t\geq 0$ of the transition semigroup associated with the solution process. Under some assumptions on the coefficients, we prove that the small time asymptotic expansion of $p_t$ is Borel summable.

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Sergio Albeverio, Boubaker Smii. 2018-10-31. Borel summation of the small time expansion of some SDE's driven by Gaussian white noise. https://arxiv.org/abs/1810.13158

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