Minimization of the Kullback information of diffusion processes. (English) Zbl 0790.60032

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.


60F10 Large deviations
60J60 Diffusion processes
60G44 Martingales with continuous parameter
60H05 Stochastic integrals
60J57 Multiplicative functionals and Markov processes
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