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Modelyuvannya Economy - Vіtlіnsky VV

3.2. Teoretichnі basis of the method of randomness modelyuvannya

Randomness modelyuvannya method (chi Monte Carlo method) - tse sposіb doslіdzhennya neviznachenih (stochastics) ekonomіchnih ob'єktіv i protsesіv, if not povnіstyu (up pevnoї mіri) vіdomimi Je vnutrіshnі vzaєmodії in Tsikh systems.

Tsey polyagaє method in the model vіdtvorennі processes for Relief stohastichnoї matematichnoї modelі that obchislennі characteristics tsogo processes. Odne TAKE vіdtvorennya mozhlivogo (vipadkovogo) will funktsіonuvannya modelovanoї Sistemi nazivayut realіzatsієyu (chi іmіtatsіynim passes; Dali - run).

Pіslya skin-passing reєstruyut sukupnіst parametrіv scho harakterizuyut vipadkovu podіyu (її realіzatsіyu). Method ґruntuєtsya on bagatokratnih runs (vipadkovih realіzatsіyah) on pіdstavі pobudovanoї modelі s away randomness opratsyuvannyam otrimanih danih s metoyu viznachennya numerical characteristics doslіdzhuvanogo ob'єkta (processes) in viglyadі randomness otsіnok yogo parametrіv. Process modelyuvannya ekonomіchnoї Sistemi zvoditsya to mashinnoї іmіtatsії doslіdzhuvanogo processes, Cauterets modelyuєtsya on AMR s usіma suttєvimi neviznachenostyami, vipadkovostyami i porodzhenim rizikom them. Іmіtatsіyne modelyuvannya nerіdko Got titles simulative modelyuvannya. Pershi vіdomostі about Monte Carlo method boule opublіkovanі in kіntsі 40th pp. XX stolіttya. The authors of the method Je amerikanskі Mathematics - ekonomіsti J. Neumann i Ulam..

Theoreticity basis of the method of randomness modelyuvannya Je law of great numbers. In teorії ymovіrnostey law of great numbers on ґruntuєtsya dovedennі low theorems for rіznih minds zbіzhnostі for ymovіrnіstyu serednіh values ​​rezultatіv (on pіdstavі velikoї kіlkostі sposterezhen) to deyakih values.

Pid law of great numbers rozumіyut kіlka theorems. Napriklad one s theorems PL Chebisheva formulyuєtsya this rite: "For neobmezhenogo zbіlshennya kіlkostі Square viprobuvan (n) serednє arithmeticity vіlnih od systematically pomilok i rіvnotochnih rezultatіv sposterezhen x i vipadkovoї quantities x, yak Got skіnchennu dispersіyu D (x), zbіgaєtsya for ymovіrnіstyu up ically mathematical spodіvannya m x = m (x) tsієї vipadkovoї magnitude. "

Tse mozhna zapisati as follows:

(3.1)

de e - yak zavgodno mala dodatne number.

Theorem Bernullі formulyuєtsya as follows: "For neobmezhenogo zbіlshennya Square sprob number (n) for some i quiet themselves minds vіdnosna frequency nastannya vipadkovoї podії zbіgaєtsya for ymovіrnіstyu to p, tobto:

(3.2)

de e - yak zavgodno mala dodatne number. "

Zgіdno tsієyu s theorem for otrimannya ymovіrnostі pevnoї podії, napriklad іmovіrnostі stanіv deyakoї Sistemi , Obchislyuyut vіdnosnі frequency now for kіlkostі realіzatsіy scho dorіvnyuє n. Result userednyuyut i s deyakim nablizhennyam oderzhuyut shukanі ymovіrnostі stanіv system. Chim bіlshim bude n, tim bude tochnіshim result obchislennya Tsikh іmovіrnostey. Tse is easy to carry.

Pripustimo, scho treba vіdshukati values ically mathematical spodіvannya m to pevnoї vipadkovoї value. Pіdberemo Taku vipadkovu value of x, dwellers

M (x) = m, and D (x) = b 2,

de b 2 - dovіlne values dispersії vipadkovoї quantities x.

Rozglyanmo poslіdovnіst n Square vipadkovih values , Rozpodіl іmovіrnostey yakih zbіgaєtsya s rozpodіlom x. Yakscho n Je dosit great, the zgіdno s central limit theorems rozpodіl sumi

bude priblizno Normal rozpodіlom s parameters a = n • m; s2 = n • b 2.

H rule "troh Sigma" viplivaє scho

(3.3)

Rozdіlivshi nerіvnіst scho roztashovana fіgurnih at the bow, on the n, h otrimaєmo ekvіvalentnu nerіvnіst tієyu samoyu ymovіrnіstyu:

Tse spіvvіdnoshennya mozhna zapisati in viglyadі:

(3.4)

Spіvvіdnoshennya (3.4) viznachaє method obchislennya serednogo value m i otsіnku pohibki. W (3.4) shows scho serednє arithmeticity realіzatsіy vipadkovoї value of x nablizheno dorіvnyuvatime number m. W іmovіrnіstyu p = 0.997 pohibka such nablizhennya not perevischuє . Obviously, scho tsya pohibka pryamuє zero Zi zrostannyam the n, scho Bulo th potrіbno bring.

Rozv'yazuvannya problems by randomness modelyuvannya polyagaє in this:

• opratsyuvannya th pobudova strukturnoї diagram of processes, mainly viyavlennya vzaєmozv'yazkіv;
• formalіzovany Opis processes;
• modelyuvannya vipadkovih yavisch (vipadkovih podіy, vipadkovih values ​​vipadkovih funktsіy), scho pritamannі doslіdzhuvanіy sistemі;
• modelyuvannya funktsіonuvannya Process Systems (pіdstavі vikoristannya danih scho otrimanі on poperednomu etapі) - vіdtvorennya processes vіdpovіdno to rozroblenoї strukturnoї schemes i formalіzovanogo inventory (іmіtatsіynі run);
• nakopichennya rezultatіv modelyuvannya (іmіtatsіynih progonіv), randomness opratsyuvannya, analіz that іnterpretatsіya їh.

Zaznachimo, scho whether SSMSC tverdzhennya stosovno to modelovanoї characteristics Sistemi povinnі ґruntuvatisya the results vіdpovіdnih perevіrok for Relief metodіv matematichnoї statistics.

Oskіlki vipadkovі podії th vipadkovі funktsії mozhut podavatisya s vikoristannyam vipadkovih values, the second modelyuvannya vipadkovih podіy i vipadkovih funktsіy held for Relief vipadkovih values.