Probability Towards 2000

ISBN-13: 9780387984582 / Angielski / Miękka / 1998 / 356 str.

Luigi Accardi; C. C. Heyde; L. Accardi

Opis

Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.

Spis treści

Non-linear extensions of classical and quantum stochastic calculus and essentially infinite dimensional analysis.- Trends and open problems in the theory of random dynamical systems.- Probability and Statistics: Selfdecomposability, finance and turbulence.- Some thoughts on extreme values.- Stochastic positive flows and quantum filtering dynamics.- Stein’s method: Some perspectives with applications.- Trilogy of couplings and general formulas for lower bound of spectral gap.- Stochasticity and chaos.- Decoupling inequalities: A second generation of martingale inequalities.- Stochastic differential equations on manifolds.- Extending flows of classical Markov processes to quantum flows in Foch space.- Quantum stochastic analysis after four decades.- Perfect simulation for the area interaction point-process.- Quantum probability seen by a classical probabilist.- Stochastic anticipating calculus.- Foundation of entropy, complexity and fractals in quantum systems.- Dirichlet forms on infinite dimensional ‘manifold-like’ state spaces: A survey of recent results and some prospects for the future.- Quantum stochastic calculus and applications — a review.- Coupling.- Some recent developments for queueing networks.