Refine
Has Fulltext
- yes (12)
Year of publication
- 2014 (12) (remove)
Document Type
- Preprint (12) (remove)
Language
- English (12)
Is part of the Bibliography
- yes (12)
Keywords
- singular perturbation (2)
- Fredholm property (1)
- Hölder-type source condition (1)
- Infinite-dimensional SDE (1)
- Lamé system (1)
- Morse-Smale property (1)
- Peano phenomena (1)
- Runge-Kutta methods (1)
- Toeplitz operators (1)
- asymptotic methods (1)
Institute
- Institut für Mathematik (12) (remove)
We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.