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- Title
L<sub>1</sub> and L<sub>∞</sub> stability of transition densities of perturbed diffusions.
- Authors
Bitter, Ilya; Konakov, Valentin
- Abstract
In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.
- Subjects
DIFFUSION coefficients; DENSITY
- Publication
Random Operators & Stochastic Equations, 2021, Vol 29, Issue 4, p287
- ISSN
0926-6364
- Publication type
Article
- DOI
10.1515/rose-2021-2067