Abstract
ABSTRACT In this article, we are interested in studying the transition density function of the couple given by the first hitting time of a fixed threshold by a one-dimensional uniformly elliptic diffusion process and the associated stopped process. Our strategy relies on the parametrix technique applied to the related semigroup. It notably allows us to extend standard PDEs results on Green and Poisson functions, see e.g. Garroni and Menaldi [Green functions for second order parabolic integro-differential problems, volume 275 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992], by establishing the infinite expansion of the corresponding transition density for irregular coefficients, here bounded measurable drift coefficient and bounded η-Hölder-continuous diffusion coefficient. As a by-product, we establish some Gaussian upper estimates.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
