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  • Aida, Shigeki; Kawabi, Hiroshi. Short time asymptotics of a certain infinite dimensional diffusion process. Stochastic analysis and related topics, VII (Kusadasi, 1998), 77--124, Progr. Probab., 48, Birkhäuser Boston, Boston, MA, 2001. MR1915450
  • Aida, Shigeki; Zhang, Tusheng. On the small time asymptotics of diffusion processes on path groups. Potential Anal. 16 (2002), no. 1, 67--78. MR1880348
  • Bao, J., Wang, F.-Y. and Yuan, C.: Derivative formula and Harnack inequality for degenerate functional SDEs. to appear in phStochastics and Dynamics.
  • Bobkov, Sergey G.; Gentil, Ivan; Ledoux, Michel. Hypercontractivity of Hamilton-Jacobi equations. J. Math. Pures Appl. (9) 80 (2001), no. 7, 669--696. MR1846020
  • Es-Sarhir, Abdelhadi; von Renesse, Max-K.; Scheutzow, Michael. Harnack inequality for functional SDEs with bounded memory. Electron. Commun. Probab. 14 (2009), 560--565. MR2570679
  • Fang, Shizan; Zhang, Tusheng. A study of a class of stochastic differential equations with non-Lipschitzian coefficients. Probab. Theory Related Fields 132 (2005), no. 3, 356--390. MR2197106
  • Gong, Fu-Zhou; Wang, Feng-Yu. Heat kernel estimates with application to compactness of manifolds. Q. J. Math. 52 (2001), no. 2, 171--180. MR1838361
  • Guo, H., Philipowski, R. and Thalmaier, A.: An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions. Preprint.
  • Hofmanová, Martina; Seidler, Jan. On weak solutions of stochastic differential equations. Stoch. Anal. Appl. 30 (2012), no. 1, 100--121. MR2870529
  • Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. Second edition. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. xvi+555 pp. ISBN: 0-444-87378-3 MR1011252
  • Lan, Guang Qiang. Pathwise uniqueness and non-explosion of SDEs with non-Lipschitzian coefficients. (Chinese) Acta Math. Sinica (Chin. Ser.) 52 (2009), no. 4, 731--736. MR2582073
  • Liu, Wei; Wang, Feng-Yu. Harnack inequality and strong Feller property for stochastic fast-diffusion equations. J. Math. Anal. Appl. 342 (2008), no. 1, 651--662. MR2440828
  • Mao, Xuerong. Stochastic differential equations and applications. Second edition. Horwood Publishing Limited, Chichester, 2008. xviii+422 pp. ISBN: 978-1-904275-34-3 MR2380366
  • Röckner, Michael; Wang, Feng-Yu. Harnack and functional inequalities for generalized Mehler semigroups. J. Funct. Anal. 203 (2003), no. 1, 237--261. MR1996872
  • Röckner, Michael; Wang, Feng-Yu. Log-Harnack inequality for stochastic differential equations in Hilbert spaces and its consequences. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13 (2010), no. 1, 27--37. MR2646789
  • Skorohod, A. V. On stochastic differential equations. (Russian) 1962 Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 1960) (Russian) pp. 159--168 Gosudarstv. Izdat. Političesk. i Navčn. Lit. Litovsk. SSR, Vilnius MR0203797
  • Stroock, Daniel W.; Varadhan, S. R. Srinivasa. Multidimensional diffusion processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 233. Springer-Verlag, Berlin-New York, 1979. xii+338 pp. ISBN: 3-540-90353-4 MR0532498
  • Taniguchi, Takeshi. Successive approximations to solutions of stochastic differential equations. J. Differential Equations 96 (1992), no. 1, 152--169. MR1153313
  • Taniguchi, Takeshi. The existence and asymptotic behaviour of solutions to non-Lipschitz stochastic functional evolution equations driven by Poisson jumps. Stochastics 82 (2010), no. 4, 339--363. MR2739602
  • Truman, Aubrey; Wang, FengYu; Wu, JiangLun; Yang, Wei. A link of stochastic differential equations to nonlinear parabolic equations. Sci. China Math. 55 (2012), no. 10, 1971--1976. MR2972624
  • Wang, Feng-Yu. Logarithmic Sobolev inequalities on noncompact Riemannian manifolds. Probab. Theory Related Fields 109 (1997), no. 3, 417--424. MR1481127
  • Wang, Feng-Yu. Harnack inequalities for log-Sobolev functions and estimates of log-Sobolev constants. Ann. Probab. 27 (1999), no. 2, 653--663. MR1698947
  • Wang, Feng-Yu. Harnack inequalities on manifolds with boundary and applications. J. Math. Pures Appl. (9) 94 (2010), no. 3, 304--321. MR2679029
  • Wang, Feng-Yu. Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds. Ann. Probab. 39 (2011), no. 4, 1449--1467. MR2857246
  • Wang, Feng-Yu; Yuan, Chenggui. Harnack inequalities for functional SDEs with multiplicative noise and applications. Stochastic Process. Appl. 121 (2011), no. 11, 2692--2710. MR2832420
  • Yamada, Toshio; Watanabe, Shinzo. On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 1971 155--167. MR0278420

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