Infinite-dimensional analysis and quantum theory as semimartingale calculus

Abstract

CONTENTS Introduction §1. Dirichlet forms. Dirichlet operators §2. Energy forms. Classical Dirichlet forms §3. Capacities. Quasi-regular Dirichlet forms and their regularizations §4. Sub-Markovian semigroups and diffusion processes generated by Dirichlet operators §5. Stochastic equations for processes generated by Dirichlet operators §6. Brownian motion with a drift in a Hilbert space §7. Conditions for functions from a given family to be logarithmic derivatives of a measure §8. Construction of a measure from its logarithmic derivatives §9. Stochastic representation of elements of L2(X,μ) and operations on them Conclusion References