I. General analysis of random perturbations. - 1. 1. Convergence of invariant measures. - 1. 2. Entropy via random perturbations: generalities. - 1. 3. Locating invariant sets. - 1. 4. Attractors and limiting measures. - 1. 5. Attractors and limiting measures via large deviations. - II. Random perturbations of hyperbolic and expanding transformations. - 2. 1. Preliminaries. - 2. 2. Markov chains in tangent bundles. - 2. 3. Hyperbolic and expanding transformations. - 2. 4. Limiting measures. - 2. 5. Sinai-Bowen-Ruelle's measures. Discussion. - 2. 6. Entropy via random perturbations. - 2. 7. Stability of the topological pressure. - 2. 8. Appendix: proof of (1. 12). - III. Applications to partial differential equations. - 3. 1. Principal eigenvalue and invariant sets. - 3. 2. Localization theorem. - 3. 3. Random perturbations and spectrum. - IV. Random perturbations of some special models. - 4. 1. Random perturbations of one-dimensional transformations. - 4. 2. Misiurewicz's maps of an interval. - 4. 3. Lorenz's type models. Language: English