<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1-Dimension It\303\264 formula</Font></Text-field>

Suppose F=F(x,t)

where dx=adt+bdW

Procedure for 1-dimension It\303\264 formula is

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=

QyQ+SSVpdG8xRzYiZio2JkkiRkdGJUkieEdGJUkiYUdGJUkiYkdGJUYlRiVGJSwmKiYsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQ5JEkidEdGJSIiIiomOSZGNS1GMDYkRjM5JUY1RjUqJjknRjUtRjA2JEYzLUkiJEdGMTYkRjoiIiNGNSNGNUZCRjVJI2R0R0YlRjVGNSooRjxGNUY4RjVJI2RXR0YlRjVGNUYlRiVGJSEiIg==

print(); # input placeholder

<Text-field style="Heading 2" layout="Heading 2">Example</Text-field>

Proof that

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

is the solution of the equation

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSNkeUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GIzYmLUYsNiVRKSZsYW1iZGE7RicvRjVGQkY+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNGaG4tRiw2JVEkeWRXRidGNEY3Rj5GK0Y+RitGPg==

y(0)=1

We use ito1 procedure as follow

QyY+SSJ5RzYiLUkkZXhwR0YlNiMsJiomSSdsYW1iZGFHRiUiIiJJIldHRiVGLEYsKiZGKyIiI0kidEdGJUYsIyEiIkYvRiw+SSNkeUdGJS1JJWl0bzFHRiU2JkYkRi0iIiFGLEYs

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJiomSSdsYW1iZGFHRiciIiJJIldHRidGLEYsKiZGKyIiI0kidEdGJ0YsIyEiIkYv

KihJJ2xhbWJkYUc2IiIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCYqJkYjRiVJIldHRiRGJUYlKiZGIyIiI0kidEdGJEYlIyEiIkYwRiVJI2RXR0YkRiU=

<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2-Dimension It\303\264 formula</Font></Text-field>

And here is the procedure for It\303\264 formula for 2 - dimensions case

Suppose F=F(x,y,t)

where

dx=adt+bdw

dy=cdt+dw

QyQ+SSVpdG8yRzYiZio2KUkiZkdGJUkieEdGJUkiYUdGJUkiYkdGJUkieUdGJUkiY0dGJUkiZEdGJUYlRiVGJSwmKiYsLi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQ5JEkidEdGJSIiIiomOSZGOC1GMzYkRjY5JUY4RjgqJjkpRjgtRjM2JEY2OShGOEY4KiY5JyIiIy1GMzYkRjYtSSIkR0Y0NiRGPUZFRjgjRjhGRSooRkRGODkqRjgtRjM2JUY2Rj1GQkY4RjgqJkZNRkUtRjM2JEY2LUZJNiRGQkZFRjhGS0Y4SSNkdEdGJUY4RjgqJiwmKiZGREY4RjtGOEY4KiZGTUY4RkBGOEY4RjhJI2RXR0YlRjhGOEYlRiVGJSEiIg==

<Text-field style="Heading 2" layout="Heading 2">Example</Text-field>

Considering the equation which has the form LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSh4ZG90ZG90RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYjNixGKy1GIzYmLUYsNiVRLSZ2YXJlcHNpbG9uO0YnL0Y1RkJGPi1GOzYtUTEmSW52aXNpYmxlVGltZXM7RidGPkZARkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRmpuLUYsNiVRI2YxRidGNEY3Rj4tRjs2LVEiK0YnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0Zjby1GIzYmLUklbXN1cEdGJDYlRlgtSSNtbkdGJDYkUSIyRidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGZm4tRiw2JVEjZjJGJ0Y0RjdGPi1GOzYtUSgmbWludXM7RidGPkZARkNGRUZHRklGS0ZNRmJvRmRvLUYjNiYtRmhvNiUtRiw2JVEoJm9tZWdhO0YnRmVuRj5Gam9GXnBGZm4tRiw2JVEieEYnRjRGN0Y+Rl9vLUYjNihGWEZmbi1GLDYlUSgmc2lnbWE7RidGZW5GPkZmbi1GLDYlUSZ4aWRvdEYnRjRGN0Y+RitGPkYrRj5GK0Y+

The solution of the linear system (when \316\265=0) has the form

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

where 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

It is easy to show that from the system above, we have

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkmbXNxcnRHRiQ2Iy1GIzYnRistRiM2JC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGNEY3LUkjbW5HRiQ2JFEiMkYnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4tRjs2LVEiK0YnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0Zmby1JJm1mcmFjR0YkNigtRiM2JC1GZm42JS1GLDYlUSV4ZG90RidGNEY3RltvRl9vRj4tRiM2JkYrLUYjNiQtRmZuNiUtRiw2JVEoJm9tZWdhO0YnL0Y1RkJGPkZbb0Zfb0Y+RitGPi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYXEvJSliZXZlbGxlZEdGQkY+Rj5GK0Y+

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

Use ito2 procedure to calculate It\303\264 difference of a and \317\206:

Calculate da, and d(\317\206)

QyYtSSdhc3N1bWVHNiI2Iy1JIj5HJSpwcm90ZWN0ZWRHNiRJImFHRiUiIiEiIiI+SSNkYUdGJS1JJWl0bzJHRiU2KS1JJXNxcnRHRiU2IywmKiRJInhHRiUiIiNGLSomSSV4ZG90R0YlRjlJJm9tZWdhR0YlISIjRi1GOEY7RixGOywoKiZJKGVwc2lsb25HRiVGLUkjZjFHRiVGLUYtKiZGQEY5SSNmMkdGJUYtRi0qKEY8RjlGK0YtLUkkY29zR0YlNiNJJHBoaUdGJUYtISIiKiZGQEYtSSZzaWdtYUdGJUYtRkk=

Qyg+SSVkcGhpRzYiLUklaXRvMkdGJTYpLUknYXJjdGFuR0YlNiMsJCooSSV4ZG90R0YlIiIiSSJ4R0YlISIiSSZvbWVnYUdGJUYxRjFGMEYuIiIhRi4sKComSShlcHNpbG9uR0YlRi9JI2YxR0YlRi9GLyomRjYiIiNJI2YyR0YlRi9GLyooRjJGOUkiYUdGJUYvLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBoaUdGJUYvRjEqJkY2Ri9JJnNpZ21hR0YlRi9GMT5GLiwkKihGPEYvRjJGLy1JJHNpbkdGJUZCRi9GMUYvPkYwKiZGPEYvRj1GL0Yv

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqKEkjYXxpckc2IiIiIkkmb21lZ2FHRiVGJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwaGlHRiVGJiEiIg==

KiZJI2F8aXJHNiIiIiItSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcGhpR0YkRiU=

QyY+SSNkYUc2Ii1JKXNpbXBsaWZ5R0YlNiNGJCEiIj5GJC1JKGNvbGxlY3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JEYkSSNkdEdGJSIiIg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqLEkoZXBzaWxvbkc2IiIiIkkjYXxpckdGJSEiIkkmb21lZ2FHRiUhIiMsKCoqRidGJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwaGlHRiVGJkYpRiZJI2YxR0YlRiYiIiMqLEYnRiZGLUYmRilGJkYkRiZJI2YyR0YlRiZGNSooRiRGJkkmc2lnbWFHRiVGNS1JJGNvc0dGL0YyRjVGKEYmSSNkdEdGJUYmI0YoRjUqLEYkRiZGKUYoRjlGJkYtRiZJI2RXR0YlRiZGKA==

Calculate d(\316\270)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVElZHBoaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKXNpbXBsaWZ5RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiRGK0Y5RjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GOQ==

QyQ+SSdkdGhldGFHNiItSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCZJJWRwaGlHRiUiIiIqJkkmb21lZ2FHRiVGLkkjZHRHRiVGLiEiIkYy

QyQ+SSdkdGhldGFHNiItSShjb2xsZWN0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRGJEkjZHRHRiUiIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqLi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSRwaGlHRikiIiJJKGVwc2lsb25HRilGLCwoKihGLUYsSSZzaWdtYUdGKSIiIy1JJHNpbkdGJkYqRixGLCoqSSNhfGlyR0YpRixJJm9tZWdhR0YpRixJI2YyR0YpRixGLUYsRiwqKEkjZjFHRilGLEY2RixGNUYsRixGLEY2ISIjRjVGOkkjZHRHRilGLCEiIiouRi1GLEYwRixGJEYsSSNkV0dGKUYsRjVGPEY2RjxGPA==

These results have been checked in "Extended first order stochastic averaging method for a class of nonlinear systems"- ND Anh - 1993

And here is the procedure which gives the Fokker-Planck equation written for the probability density function p of da, d(\316\270)

QyQ+SSNGUEc2ImYqNilJInBHRiVJInhHRiVJImFHRiVJImJHRiVJInlHRiVJImNHRiVJImRHRiVGJUYlRiUvLUklRGlmZkdGJTYkOSRJInRHRiUsLC1GMTYkKiY5JiIiIkYzRjo5JSEiIi1GMTYkKiY5KUY6RjNGOjkoRjwtRjE2JComOSciIiNGM0Y6LUkiJEclKnByb3RlY3RlZEc2JEY7RkYjRjpGRi1GMTYlKihGRUY6OSpGOkYzRjpGO0ZBRjotRjE2JComRk9GRkYzRjotRkg2JEZBRkZGS0YlRiVGJUY8

QyQtSSNGUEc2IjYpSSJwR0YlSSJhR0YlSShhbHBoYV8xR0YlSSdiZXRhXzFHRiVJJnRoZXRhR0YlSShhbHBoYV8yR0YlSSdiZXRhXzJHRiUiIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JJURpZmZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JEkicEdGKEkidEdGKCwsLUYkNiQqJkkoYWxwaGFfMUdGKCIiIkYqRjFJI2F8aXJHRighIiItRiQ2JComSShhbHBoYV8yR0YoRjFGKkYxSSZ0aGV0YUdGKEYzLUYkNiUqJkknYmV0YV8xR0YoIiIjRipGMUYyRjIjRjFGPS1GJDYlKihGPEYxSSdiZXRhXzJHRihGMUYqRjFGMkY4RjEtRiQ2JSomRkJGPUYqRjFGOEY4Rj4=