Volume 22, 2018
|Page(s)||178 - 209|
|Published online||14 December 2018|
Stochastic formulations of the parametrix method★
Department of Mathematical Sciences, Ritsumeikan University,
* Corresponding author: email@example.com
Accepted: 20 July 2018
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
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.