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Advances in Analysis, Probability and Mathematical Physics: Contributions of Nonstandard Analysis
Tag	Description
020	$a9789401584517
082	$a515
099	$aOnline Resource: Springer
245	$aAdvances in Analysis, Probability and Mathematical Physics$h[EBook]$bContributions of Nonstandard Analysis$cedited by Sergio A. Albeverio, Wilhelm A. J. Luxemburg, Manfred P. H. Wolff.
260	$aDordrecht$bSpringer Netherlands$c1995.
300	$aX, 252 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aMathematics and Its Applications ;$v314
505	$aTable of Content -- I: Analysis -- Singular traces and nonstandard analysis -- Navier-Stokes equations -- Hyperfinite approximations of commutative topological groups -- A note on the myope topology -- Nonlinear theories of generalized functions -- A nonstandard approach to the Pettis integral -- A counterexample to the spectral mapping theorem revisited from a nonstandard point of view -- Nonstandard polynominals in several variables -- An existence result for a class of partial differential equations with smooth coefficients -- On the generation of topology by external equivalence relations -- Nonstandard hulls of Lebesgue-Bochner spaces -- II: Probability Theory -- A nonstandard approach to diffusions on manifolds and nonstandard heat kernels -- A nonstandard approach to the Malliavin Calculus -- Ergodic transformations in AST -- Nonstandard characterization for a general invariance principle -- Andersons’s Brownian motion and the infinite dimensional Ornstein-Uhlenbeck process -- Two applications of NSA in the theory of stochastic dynamical systems -- Nonstandard methods and the space of experiments -- III: Mathematical Physics -- Infinite range forces and strong L1-asymptotics for the space-homogeneous Boltzmann equation -- A nonstandard analysis approach to the theory of quantum meanfield systems.
520	$aIn 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called `Nonstandard analysis'. `Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics. This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aAlbeverio, Sergio A.$eeditor.
700	$aLuxemburg, Wilhelmus A. J.$d1929-2018$eeditor.
700	$aWolff, Manfred P. H.$eeditor.
710	$aSpringerLink (Online service)
830	$aMathematics and Its Applications ;$v314
856	$uhttp://dx.doi.org/10.1007/978-94-015-8451-7