Geodesic
Limit theorems for nonhomogeneous Ornstein--Uhlenbeck process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 111-134

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We describe a construction of a summation scheme with replacements of random variables. We obtain, as a limit, a time nonhomogeneous generalization of Ornstein–Uhlenbeck process. We describe it by a transform of Lamperti type where an arbitrary continuous monotone function is used instead of the exponential one. 
@article{ZNSL_2006_339_a7,
     author = {O. V. Rusakov and A. N. Chuprunov},
     title = {Limit theorems for  nonhomogeneous {Ornstein--Uhlenbeck} process},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {111--134},
     publisher = {mathdoc},
     volume = {339},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a7/}
}
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O. V. Rusakov; A. N. Chuprunov. Limit theorems for  nonhomogeneous Ornstein--Uhlenbeck process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 111-134. http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a7/