Diffusion Processes and Related Problems in Analysis Volume II

I: Diffusion Processes and General Stochastic Flows on Manifolds. - Stability and equilibrium properties of stochastic flows of diffeomorphisms. - Stochastic flows on Riemannian manifolds. - II: Special Flows and Multipoint Motions. - Isotropic stochastic flows. - The existence of isometric stochastic flows for Riemannian Brownian motions. - Time-reversal of solutions of equations driven by Lévy processes. - Birth and death on a flow. - III: Infinite Dimensional Systems. - Lyapunov exponents and stochastic flows of linear and affine hereditary systems. - Convergence in distribution of Markov processes generated by i. i. d. random matrices. - IV: Invariant Measures in Real and White Noise-Driven Systems. - Remarks on ergodic theory of stochastic flows and control flows. - Stochastic bifurcation: instructive examples in dimension one. - Lyapunov exponent and rotation number of the linear harmonic oscillator. - The growth of energy of a free particle of small mass with multiplicative real noise. - V: Iterated Function Systems. - Iterated function systems and multiplicative ergodic theory. - Weak convergence and generalized stability for solutions to random dynamical systems. - Random affine iterated function systems: mixing and encoding. Language: English