...quations, probability theory, and others. The basic method of non-standard analysis can roughly be described as follows. One considers a certain mathematical s
...initesimal calculus]]) which in the subsequent development of mathematical analysis was rejected in favour of the precise concept of the limit of a variable qu
5 KB (677 words) - 23:47, 29 April 2012
...ad, R. Høegh-Krohn, T. Lindstrøm, "Nonstandard methods in stochastic analysis and mathematical physics" , Acad. Press (1986)</TD></TR></table>
3 KB (421 words) - 08:29, 6 June 2020
In stochastic analysis, the principle of "differentiation" of random functions, or [[Itô formul
...Fenstad, R. Høegh-Krohn, T. Lindstrøm, "Nonstandard methods in stochastic analysis and mathematical physics" , Acad. Press (1986)</TD></TR>
6 KB (900 words) - 17:54, 16 July 2024
...p">[a5]</TD> <TD valign="top"> P.A. Samuelson, "Foundations of economic analysis" , Harvard Univ. Press (1947)</TD></TR>
<TR><TD valign="top">[a7]</TD> <TD valign="top"> H. Skala, "Nonstandard utilities and the foundations of game theory" ''Internat. J. Game Theory''
5 KB (854 words) - 09:14, 7 April 2018
...initely-large variable magnitudes is a fundamental concept in mathematical analysis. The idea which was held prior to the modern approach to the concept of the
which satisfies many needs in analysis and in the theory of functions of a real variable. The same applies to the
10 KB (1,463 words) - 22:12, 5 June 2020
$#C+1 = 125 : ~/encyclopedia/old_files/data/M062/M.0602610 Mathematical analysis
...of an infinitesimal quantity, therefore it could be said that mathematical analysis studies functions and their generalizations by infinitesimal methods.
19 KB (2,844 words) - 08:57, 13 January 2024
[[Category:Stochastic analysis]]
...Fenstad, R. Høegh-Krohn, T. Lindstrøm, "Nonstandard methods in stochastic analysis and mathematical physics" , Acad. Press (1986) {{MR|0859372}} {{ZBL|0605.60
10 KB (1,420 words) - 19:10, 9 January 2024
...pace is standard; for uncountably many factors the product is perfect but nonstandard. The one-dimensional [[Hausdorff measure]] on the plane is not σ-finite.
...iscrete space cannot be atomless (unless $\mu(X)=0$), but a purely atomic nonstandard space can be continuous. (See {{Cite|B|Sect. 7.14(v)}}.)
15 KB (2,431 words) - 07:07, 23 September 2012
A term which formerly included various branches of mathematical analysis connected with the concept of an [[Infinitely-small function|infinitely-sma
...><TD valign="top">[a8]</TD> <TD valign="top"> A. Robinson, "Nonstandard analysis" , North-Holland (1966)</TD></TR><TR><TD valign="top">[a9]</TD> <TD valign
22 KB (3,357 words) - 17:34, 1 January 2021
The phrase "arithmetization of analysis" refers to 19th century efforts to create a "theory of real numbers ... usi
...the arithmetization program signified efforts to develop a foundation for analysis, i.e. the calculus, in terms of the natural numbers
91 KB (14,186 words) - 16:58, 23 November 2023
...also been developed using methods of [[Non-standard analysis|non-standard analysis]] [[#References|[a7]]].
...ad, R. Høegh-Krohn, T. Lindstrøm, "Nonstandard methods in stochastic analysis and mathematical physics" , Acad. Press (1986)</TD></TR><TR><TD valign="to
107 KB (14,649 words) - 21:43, 15 December 2020
...l calculus in the large|Variational calculus in the large]] for the global analysis problems that emerged later. For the much related topic of optimal control,
...</TR><TR><TD valign="top">[a20]</TD> <TD valign="top"> J. Hirschfeld, "The nonstandard treatment of Hilbert's fifth problem" ''Trans. Amer. Math. Soc.'' , '''321'
29 KB (4,109 words) - 19:54, 18 March 2018