View source for Talk:Gaussian measure

Gaussian measures are the natural starting point for various Gaussian random processes (and fields). However, we have no article on Gaussian measures, and a rather obsolete article on [[Gaussian process]]es.

"Gaussian random variables and processes always played a central role  in the probability theory and statistics. The modern theory of Gaussian  measures combines methods from probability theory, analysis, geometry  and topology and is closely connected with diverse applications in  functional analysis, statistical physics, quantum field theory,  financial mathematics and other areas." {{Cite|L}}

"The  modern theory of Gaussian measures lies at the intersection of the  theory of random processes, functional analysis, and mathematical  physics and is closely connected with diverse applications in quantum  field theory, statistical physics, financial mathematics, and other  areas of sciences. The study of Gaussian measures combines ideas and  methods from probability theory, nonlinear analysis, geometry, linear  operators, and topological vector spaces in a beautiful and nontrivial  way." {{Cite|B|Preface}}

"Gaussian processes have a rich, detailed and very well understood general theory, which makes them beloved by theoreticians.
In   applications [...] it is important to have specific, explicit formulae   that allow one to predict, to compare theory with experiment, etc. As  we  shall see [...] it will be only for Gaussian (and related [...])  fields  that it is possible to derive such formulae in the setting of  excursion  sets." {{Cite|AT}}

{|
|valign="top"|{{Ref|B}}|| V.I. Bogachev, "Gaussian measures",   AMS (1998).  {{MR|1642391}} {{ZBL|0913.60035}}
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|valign="top"|{{Ref|L}}||  R. Latała, "On some inequalities for Gaussian measures", Proceedings of  the International Congress of Mathematicians (2002), 813-822.  {{MR|1957087}}  {{ZBL|1015.60011}}
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|valign="top"|{{Ref|AT}}|| R.J. Adler, J.E. Taylor, "Random fields and geometry", Springer (2007).  {{MR|2319516}} {{ZBL|1149.60003}}
|}

--[[User:Boris Tsirelson|Boris Tsirelson]] 22:12, 14 June 2012 (CEST)