Stochastic Processes and Their Applications

'Et moi,., si j'avait su comment en revenIT, One service mathematics has rendered the je n'y serais point allt\.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics.:; 'One service logic has rendered com­ puter science.:; 'One service category theory has rendered mathematics.:. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

InhaltsangabeStochastic stability for vector fields with a manifold of singular points, and an application to lattice gauge theory.- Ricci curvature and dimension for diffusion semigroups.- The Zitterbewegung of a Dirac electron in a central field.- Maximum entropy principles for Markov processes.- An optimal Carleman-type inequality for the Dirac operator.- Toeplitz operators - an asymptotic quantization of symplectic cones.- Perturbation theory for random disordered systems.- On rigorous hydrodynamics, self-diffusion and the Green-Kubo formulae.- A stochastic model for plasma dynamics.- Macroscopic potentials of dissipative dynamical systems.- Random-path intersections in geometry, probability and physics.- Noncummutative version of the central limit theorem and of Cramér's theorem.- Distributions, Sobolev spaces on Gaussian vector spaces and Ito's calculus.- On problems in stochastic differential equations connected with some particular type of interacting particles.- Asymptotic behaviors of moments for one-dimensional generalized diffusion processes.- Langevin equation and fluctuation-dissipation theorem.- The Dirichlet problem for quasi-linear partial differential operators with boundary data given by a distribution.- Stationary stochastic perturbation of a linear delay equation.- Random lattice models.- Interactions galileennes aimant-charge.- The polaron functional integral.- The Bosonic string.