{"content":[{"text":"Log-Harnack Inequality for Stochastic \n Diﬀerential Equations in Hilbert Spaces and \n its Consequences∗","bbox":{"left":0.119505,"top":0.193989,"width":0.7375710000000001,"height":0.09038300000000002}},{"text":"R¨ocknerb),c) Wanga),d)† \n Michael and Feng-Yu \n a)School of Math. Sci. & Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China \n b)Department of Mathematics, Bielefeld University, D-33501 Bielefeld, Germany \n c)Department of Mathematics and Statistics, Purdue University, W. Lafayette, IN 47907, USA \n d)Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK","bbox":{"left":0.133724,"top":0.3025,"width":0.709058,"height":0.11247700000000005}},{"text":"November 3, 2009","bbox":{"left":0.398294,"top":0.433657,"width":0.17984300000000003,"height":0.01813199999999998}},{"text":"Abstract \n A logarithmic type Harnack inequality is established for the semigroup of solu- \n tions to a stochastic diﬀerential equation in Hilbert spaces with non-additive noise. \n As applications, the strong Feller property as well as the entropy-cost inequality for \n the semigroup are derived with respect to the corresponding distance (cost func- \n tion).","bbox":{"left":0.165466,"top":0.503284,"width":0.645526,"height":0.108989}},{"text":"AMS subject Classiﬁcation: 60J60, 58G32. \n Keywords: Stochastic diﬀerential equation, log-Harnack inequality, strong Feller property, \n entropy-cost inequality.","bbox":{"left":0.117647,"top":0.629569,"width":0.7412029999999998,"height":0.051587999999999856}},{"text":"1","bbox":{"left":0.117647,"top":0.760322,"width":0.01583699999999999,"height":0.021758000000000055}},{"text":"Introduction","bbox":{"left":0.16513,"top":0.760322,"width":0.174236,"height":0.021758000000000055}},{"text":"Under a curvature condition the second named author established the following type \n dimension-free Harnack inequality for diﬀusion semigroups on a Riemannian manifold M \n ([14]):","bbox":{"left":0.117647,"top":0.798492,"width":0.7411639999999999,"height":0.051590000000000025}},{"text":"∗Supported in part by WIMCS, NNSFC(10721091) and the 973-Project. \n †Corresponding author. wangfy@bnu.edu.cn; F.Y.Wang@swansea.ac.uk","bbox":{"left":0.139466,"top":0.861664,"width":0.516895,"height":0.031208000000000014}},{"text":"1","bbox":{"left":0.483407,"top":0.915478,"width":0.009572000000000025,"height":0.015109999999999957}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}