Geodesic
Stochastic formulations of the parametrix method
ESAIM: Probability and Statistics, Tome 22 (2018), pp. 178-209

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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 L p ( 𝐑 d ) , 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.

DOI : 10.1051/ps/2018013
Classification : 2010, 60H07
Keywords: Stochastic differential equation, singular drift, density function, Gaussian two-sided bounds, parametrix method

Kohatsu-Higa, Arturo 1 ; Yûki, Gô 1

1 
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     title = {Stochastic formulations of the parametrix method},
     journal = {ESAIM: Probability and Statistics},
     pages = {178--209},
     publisher = {EDP-Sciences},
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     year = {2018},
     doi = {10.1051/ps/2018013},
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     zbl = {1403.60047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2018013/}
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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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