TAILIEUCHUNG - Error Calculus for Finance and Physics: The Language of Dirichlet Forms

Our primary objective herein is not to determine how approximate calculations introduce errors into situations with accurate hypotheses, but instead to study how rigorous calculations transmit errors due to inaccurate parameters or hypotheses. Unlike quantities represented by entire numbers, the continuous quantities generated from physics, economics or engineering sciences, as represented by one or several real numbers, are compromised by errors. The choice of a relevant mathematical language for speaking about errors and their propagation is an old topic and one that has incited a large variety of works. Without retracing the whole history of these investigations, we can draw the main lines of the present inquiry | de Gruyter Expositions in Mathematics 37 Editors O. H. Kegel Albert-Ludwigs-Universitat Freiburg V. P. Maslov Academy of Sciences Moscow W. D. Neumann Columbia University New York R. Jr. Rice University Houston de Gruyter Expositions in Mathematics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 The Analytical and Topological Theory of Semigroups K. H. Hofmann J. D. Lawson J. S. Pym Eds. Combinatorial Homotopy and 4-Dimensional Complexes H. J. Baues The Stefan Problem A. M. Meirmanov Finite Soluble Groups K. Doerk T. O. Hawkes The Riemann Zeta-Function A. A. Karatsuba S. M. Voronin Contact Geometry and Linear Differential Equations V. E. Nazaikinskii V. E. Shatalov B. Yu. Sternin Infinite Dimensional Lie Superalgebras Yu. A. Bahturin A. A. Mikhalev V. M. Petrogradsky M. V. Zaicev Nilpotent Groups and their Automorphisms E. I. Khukhro Invariant Distances and Metrics in Complex Analysis M. Jarnicki P. Pflug The Link Invariants of the Chern-Simons Field Theory E. Guadagnini Global Affine Differential Geometry of Hypersurfaces . Li U. Simon G. Zhao Moduli Spaces of Abelian Surfaces Compactification Degenerations and Theta Functions K. Hulek C. Kahn S. H. Weintraub Elliptic Problems in Domains with Piecewise Smooth Boundaries S. A. Nazarov B. A. Plamenevsky Subgroup Lattices of Groups R. Schmidt Orthogonal Decompositions and Integral Lattices A. I. Kostrikin P. H. Tiep The Adjunction Theory of Complex Projective Varieties M. C. Beltrametti A. J. Sommese The Restricted 3-Body Problem Plane Periodic Orbits A. D. Bruno Unitary Representation Theory of Exponential Lie Groups H. Leptin J. Ludwig Blow-up in Quasilinear Parabolic Equations A. A. Samarskii . Galaktionov S. P. Kurdyumov A. P. Mikhailov Semigroups in Algebra Geometry and Analysis K. H. Hofmann J. D. Lawson E. B. Vinberg Eds. Compact Projective Planes H. Salzmann D. Betten T. Grundhofer H. Hăhl R. Lowen M. Stroppel An Introduction to Lorentz .

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