caa a22 4500 475839412 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1010719902298 doi (NATIONALLICENCE)springer-10.1023/A:1010719902298 A White-Noise Approach to Stochastic Calculus [Elektronische Daten] [Luigi Accardi, Yun Lu, Igor Volovich] During the past 15 years a new technique, called the stochastic limit of quantum theory, has been applied to deduce new, unexpected results in a variety of traditional problems of quantum physics, such as quantum electrodynamics, bosonization in higher dimensions, the emergence of the noncrossing diagrams in the Anderson model, and in the large-N-limit in QCD, interacting commutation relations, new photon statistics in strong magnetic fields, etc. These achievements required the development of a new approach to classical and quantum stochastic calculus based on white noise which has suggested a natural nonlinear extension of this calculus. The natural theoretical framework of this new approach is the white-noise calculus initiated by T. Hida as a theory of infinite-dimensional generalized functions. In this paper, we describe the main ideas of the white-noise approach to stochastic calculus and we show that, even if we limit ourselves to the first-order case (i.e. neglecting the recent developments concerning higher powers of white noise and renormalization), some nontrivial extensions of known results in classical and quantum stochastic calculus can be obtained. Kluwer Academic Publishers, 2000 quantum probability nationallicence white noise nationallicence stochastic limit nationallicence Accardi Luigi Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut Lu Yun Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut Volovich Igor Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 3-25 0167-8019 63:1-3<3 2000 63 10440 https://doi.org/10.1023/A:1010719902298 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1010719902298 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Accardi Luigi Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut NATIONALLICENCE 700 1- Lu Yun Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut NATIONALLICENCE 700 1- Volovich Igor Centro Matematico Vito Volterra, Università di Roma, 00133, Rome, Italy. e-mail aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 3-25 0167-8019 63:1-3<3 2000 63 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer