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

Article type: Research Article

Authors: Albeverio, Sergio^{a; b} | Smii, Boubaker^{c; *}

Affiliations: [a] Department of Applied Mathematics and HCM, BiBoS, IZKS, University of Bonn, Germany | [b] CERFIM, Locarno, Switzerland. E-mail: [email protected] | [c] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider stochastic differential equations with a drift term of gradient type and driven by Gaussian white noise on Rd. Particular attention is given to the kernel pt, t>0 of the transition semigroup associated with the solution process. Under some rather strong regularity and growth assumptions on the coefficients, we adapt previous work by Thierry Hargé on Schrödinger operators and prove that the small time asymptotic expansion of pt, t>0 is Borel summable. We also briefly indicate some extensions and applications.

Keywords: SDEs, asymptotic expansions, Borel summability

DOI: 10.3233/ASY-191525

Journal: Asymptotic Analysis, vol. 114, no. 3-4, pp. 211-223, 2019