A large deviation principle for small perturbations of random evolution equations in Hoelder norm
Large deviation estimates of Wentzell-Freidlin type in Hölder norms with exponent \(\alpha <\frac {1}{2}\) for a stochastic differential equation of the form \[ dX^\varepsilon (t)=b(X^\varepsilon (t),Y(t))+\varepsilon ^{1/2}\sigma (X^\varepsilon (t))dW(t), \qquad x^\varepsilon (0)=x, \] are proved where \(W(t)\) is a standard Brownian motion and \(Y(t)\) is a random process independent of \(W\). The coefficients \(b:R^d\times R^m \to R^d\) and \(\sigma :R^d\to M_{d\times d}\) are assumed to be Lipschitz continuous and bounded, the diffusion matrix is uniformly positive definite. For analogous results for diffusion processes cf. \textit{P. Baldi, G. Ben Arous} and \textit{G. Kerkyacharian} [Stochastic Processes Appl. 42, No. 1, 171-180 (1992; Zbl 0757.60014)].
scientific article; zbMATH DE number 1134836
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