Title | Real and Stochastic Analysis [electronic resource] : New Perspectives / edited by M. M. Rao |
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Imprint | Boston, MA : Birkhรคuser Boston, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2054-1 |
Descript | X, 406 p. online resource |
and Outline -- References -- Stochastic Differential Equations and Hypoelliptic Operators -- 1 Introduction -- 2 Integration by parts and the regularity of induced measures -- 3 A Hรถrmander theorem for infinitely degenerate operators -- 4 A study of a class of degenerate functional stochastic differential equations -- 5 Some open problems -- References -- Curved Wiener Space Analysis -- 1 Introduction -- 2 Manifold primer -- 3 Riemannian geometry primer -- 4 Flows and Cartan's development map -- 5 Stochastic calculus on manifolds -- 6 Heat kernel derivative formula -- 7 Calculus on W(M) -- 8 Malliavin's methods for hypoelliptic operators -- 9 Appendix: Martingale and SDE estimates -- References -- Noncommutative Probability and Applications -- 1 Introduction -- 2 Traditional probability theory -- 3 Unsharp traditional probability theory -- 4 Sharp quantum probability -- 5 Unsharp quantum probability -- 6 Effects and observables -- 7 Statistical maps -- 8 Sequential products on Hilbert space -- 9 Quantum operations -- 10 Completely positive maps -- 11 Sequential effect algebras -- 12 Further SEA results -- References -- Advances and Applications of the Feynman Integral -- 1 Introduction -- 2 The operator valued Feynman integral -- 3 Evolution processes -- 4 The Feynman-Kac formula -- 5 Boundedness of processes -- 6 Path integrals on finite sets -- 7 The Dirac equation in one space dimension -- 8 Integration with respect to unbounded set functions -- 9 The Feynman integral with singular potentials -- 10 Quantum field theory -- References -- Stochastic Differential Equations Based on Lรฉvy Processes and Stochastic Flows of Diffeomorphisms -- 1 Stochastic integrals for sernimartingales -- 2 Stochastic analysis of Lรฉvy processes -- 3 Stochastic differential equation and stochastic flow -- 4 Appendix. Kolmogorov's criterion for the continuity of random fields and the uniform convergence of random fields -- References -- Convolutions of Vector Fields-III: Amenability and Spectral Properties -- 1 Introduction -- 2 Elementary Aspects of Random Walks -- 3 Role of the Spectrum of Convolution Operators -- 4 Amenable Function Algebras and Groups -- 5 Spectra of Convolution Operators and Amenability -- 6 Beurling and Segal Algebras for Amenability -- References