| Issue |
ESAIM: PS
Volume 22, 2018
|
|
|---|---|---|
| Page(s) | 178 - 209 | |
| DOI | https://doi.org/10.1051/ps/2018013 | |
| Published online | 14 December 2018 | |
Stochastic formulations of the parametrix method★
Department of Mathematical Sciences, Ritsumeikan University,
1-1-1 Nojihigashi,
Kusatsu,
Shiga
525-8577, Japan
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
6
June
2017
Accepted:
20
July
2018
Abstract
In this manuscript, we consider stochastic expressions of the parametrix method for solutions of d-dimensional stochastic differential equations (SDEs) with drift coefficients which belong to Lp(Rd), p > d. We prove the existence and Hölder continuity of probability density functions for distributions of solutions at fixed points and obtain an explicit expansion via (stochastic) parametrix methods. We also obtain Gaussian type upper and lower bounds for these probability density functions.
Mathematics Subject Classification: 2010 / 60H07
Key words: Stochastic differential equation / singular drift / density function / Gaussian two-sided bounds / parametrix method
This research has been supported by grants of the Japanese government KAKENHI 16K05215.
© EDP Sciences, SMAI 2018
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