Abstract
AbstractThe aim of this work is to prove the existence of a fundamental solution associated to the Kolmogorov equation $$\mathscr {L}u = f$$
L
u
=
f
in the dilation invariant case, with bounded measurable first order coefficients and bounded diffusion coefficients satisfying a sort of divergence free assumption. Finally, we prove Gaussian upper and lower bounds for the fundamental solution, and other related properties, under less restrictive assumptions on the coefficients.
Funder
Università Politecnica delle Marche
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference41 articles.
1. Alziary, B., Décamps, J.P., Koehl, P.F.: A P.D.E. approach to Asian options: analytical and numerical evidence. J. Bank. Financ. 21, 613–640 (1997)
2. Anceschi, F., Polidoro, S.: A survey on the classical theory for Kolmogorov equation. Matematiche 75(1), 221–258 (2020). https://doi.org/10.4418/2020.75.1.11
3. Anceschi, F., Muzzioli, S., Polidoro, S.: Existence of a fundamental solution of partial differential equations associated to Asian options. Real World Appl. 62, 103373 (2021). https://doi.org/10.1016/j.nonrwa.2021.103373
4. Anceschi, F., Rebucci, A.: A note on the weak regularity theory for degenerate Kolmogorov equations. J. Diff. Eq. 341, 538–588 (2022). https://doi.org/10.1016/j.jde.2022.09.024
5. Albritton, D., Armstrong, S., Mourrat, J.C., Novack, M.: Variational methods for the kinetic Fokker-Planck equation pre-print. arXiv:1902.04037v2 (2021)
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