Cattiaux, Patrick; Léonard, Christian Minimization of the Kullback information of diffusion processes. (English) Zbl 0790.60032 Ann. Inst. Henri Poincaré, Probab. Stat. 30, No. 1, 83-132 (1994). Summary: We compute an explicit expression for the rate function of large deviations for the measure valued empirical process \(\overline X^ N(t)={1\over N}\sum^ N_{i=1}\delta_{X_ i(t)}\), where the \(X_ i\)’s are independent copies of a diffusion process in \(\mathbb{R}^ d\). This is done by minimizing the relative entropy (Kullback information) of a probability measure \(Q\) with respect to the law \(P\) of \(X_ i\) when all marginals of \(Q\) are fixed. The finiteness of the rate function is connected with the existence of conservative diffusions, with a general diffusion matrix. These diffusion processes are constructed in very general cases. Cited in 2 ReviewsCited in 15 Documents MSC: 60F10 Large deviations 60J60 Diffusion processes 60G44 Martingales with continuous parameter 60H05 Stochastic integrals 60J57 Multiplicative functionals and Markov processes Keywords:relative entropy; Föllmer measure; Girsanov transformation; Kullback information; large deviations; measure valued empirical process; conservative diffusions PDF BibTeX XML Cite \textit{P. Cattiaux} and \textit{C. Léonard}, Ann. Inst. Henri Poincaré, Probab. Stat. 30, No. 1, 83--132 (1994; Zbl 0790.60032) Full Text: Numdam EuDML OpenURL