PreprintCC BY 4.0arXiv
Weighted derivative estimates for Kolmogorov equations
Abstract
For diffusions whose coefficients are smooth, with at most linear growth and bounded derivatives of higher order, we establish explicit pointwise bounds on the spatial derivatives of the classical solution to the Cauchy problem with polynomially growing initial data. We also obtain explicit growth estimates for the derivatives of the SDE with respect to the initial data. The proofs combine Lyapunov functions and Markov semigroups on weighted spaces with Kunita's theory of the differentiable dependence of SDE solutions on the initial data.
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BibTeX
@misc{sidorenko2026weighted,
title = {{Weighted derivative estimates for Kolmogorov equations}},
author = {Artur Sidorenko and Vasilii Kolokoltsov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13241},
eprint = {2610.13241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13241},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted derivative estimates for Kolmogorov equations
AU - Artur Sidorenko
AU - Vasilii Kolokoltsov
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13241
UR - https://arxiv.org/abs/2610.13241
AB - For diffusions whose coefficients are smooth, with at most linear growth and bounded derivatives of higher order, we establish explicit pointwise bounds on the spatial derivatives of the classical solution to the Cauchy problem with polynomially growing initial data. We also obtain explicit growth estimates for the derivatives of the SDE with respect to the initial data. The proofs combine Lyapunov functions and Markov semigroups on weighted spaces with Kunita's theory of the differentiable dependence of SDE solutions on the initial data.
ER -