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Generalized Brownian Motion, Point Processes and Stochastic Calculus for Random Fields
Author(s) -
Fichtner K.H.,
Winkler G.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931610122
Subject(s) - mathematics , probabilistic logic , point process , stochastic calculus , brownian motion , malliavin calculus , point (geometry) , representation (politics) , calculus (dental) , time scale calculus , stochastic process , simple (philosophy) , algebra over a field , mathematical analysis , pure mathematics , multivariable calculus , stochastic partial differential equation , geometry , differential equation , medicine , philosophy , statistics , dentistry , engineering , epistemology , control engineering , politics , political science , law
A representation of the Malliavian derivative and the Skorochod integral in terms of random point systems on Polish spaces (and thus generalizing from the unit interval) is derived. This leads to a stochastic calculus based on random point systems. The operators are given explicitely and in a simple form allowing concrete probabilistic and quantum probabilistic interpretations.