In this manuscript, we consider stochastic expressions of the parametrix method for solutions of -dimensional stochastic differential equations (SDEs) with drift coefficients which belong to . 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.
Keywords: Stochastic differential equation, singular drift, density function, Gaussian two-sided bounds, parametrix method
Kohatsu-Higa, Arturo 1 ; Yûki, Gô 1
@article{PS_2018__22__178_0,
author = {Kohatsu-Higa, Arturo and Y\^uki, G\^o},
title = {Stochastic formulations of the parametrix method},
journal = {ESAIM: Probability and Statistics},
pages = {178--209},
year = {2018},
publisher = {EDP Sciences},
volume = {22},
doi = {10.1051/ps/2018013},
mrnumber = {3891754},
zbl = {1403.60047},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2018013/}
}
TY - JOUR AU - Kohatsu-Higa, Arturo AU - Yûki, Gô TI - Stochastic formulations of the parametrix method JO - ESAIM: Probability and Statistics PY - 2018 SP - 178 EP - 209 VL - 22 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2018013/ DO - 10.1051/ps/2018013 LA - en ID - PS_2018__22__178_0 ER -
Kohatsu-Higa, Arturo; Yûki, Gô. Stochastic formulations of the parametrix method. ESAIM: Probability and Statistics, Tome 22 (2018), pp. 178-209. doi: 10.1051/ps/2018013
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