Geodesic
Local asymptotical normality for differently distributed observations
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 251-266

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Conditions of local asymptotical normality (LAN) are given for families of distributions for essentially inhomogeneous in time observations. A generalization of LAN to continuous observations is considered and conditions of LAN for continuous observations (4.3) are obtained. 
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     author = {I. A. Ibragimov and R. Z. Khas'minskii},
     title = {Local asymptotical normality for differently distributed observations},
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I. A. Ibragimov; R. Z. Khas'minskii. Local asymptotical normality for differently distributed observations. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 251-266. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a2/