Помогите разобраться: ДУ + тервер и матстатистика.

[sinergo]

Добрый день. Возник вопрос.. Есть такой набор ДУ

$d{N_0}(t) = [ - {k_{01}}(DR){N_0}(t) + {k_{R1}}{N_1}(t) + {M_0}(t){N_0}(t) - {k_d}{N_0}(t)]dt + {\sigma _{0,0}}\sqrt {{N_0}(t)} d{w_0}(t) + {\sigma _{0,1}}\sqrt {{N_1}(t)} d{w_1}(t);$
$d{N_1}(t) = [{k_{01}}(DR){N_0}(t) - {k_{12}}(DR){N_1}(t) + {k_{R2}}{N_2}(t) - {k_{R1}}{N_1}(t) - {k_d}{N_1}(t)]dt + {\sigma _{1,0}}\sqrt {{N_0}(t)} d{w_0}(t) + {\sigma _{1,1}}\sqrt {{N_1}(t)} d{w_1}(t) + {\sigma _{1,2}}\sqrt {{N_2}(t)} d{w_2}(t);$
$d{N_2}(t) = [{k_{12}}(DR){N_1}(t) - {k_{23}}(DR){N_2}(t) - {k_{R2}}{N_2}(t) - {k_d}{N_2}(t)]dt + {\sigma _{2,0}}\sqrt {{N_1}(t)} d{w_1}(t) + {\sigma _{2,1}}\sqrt {{N_2}(t)} d{w_3}(t);$
$d{N_3}(t) = [{k_{23}}(DR){N_2}(t) + (1 - {P_4}){M_3}(t){N_3}(t) - {P_4}{M_3}(t){N_3}(t) - {k_d}{N_3}(t)]dt + {\sigma _{3,0}}\sqrt {{N_2}(t)} d{w_3}(t) + {\sigma _{3,1}}\sqrt {{N_3}(t)} d{w_4}(t); $
$d{N_4}(t) = [{P_4}{M_3}{N_3}(t) + ({M_4} - {k_d}){N_4}(t)]dt + {\sigma _{4,0}}\sqrt {{N_3}(t)} d{w_4}(t) + {\sigma _{4,1}}\sqrt {{N_4}(t)} d{w_5}(t).$


На основании этой системы надо найти моменты перого и второго порядка. Я делаю на основе формулы Ито, но очень сильно сомневаюсь в результате :( Получилось вот такое:


$dE{N_0}(t) = [( - {k_{01}} + {M_0} - {k_d})E{N_0}(t) + {k_{R1}}E{N_1}(t)]dt$
$dE{N_1}(t) = [{k_{01}}E{N_0}(t)dt + ( - {k_{12}} - {k_{R1}} - {k_d})E{N_1}(t) + {k_{R2}}E{N_2}(t)]dt$
$dE{N_2}(t) = [{k_{12}}E{N_1}(t) + ( - {k_{23}} - {k_{R2}} - {k_d})E{N_2}(t)]dt$
$dE{N_3}(t) = [{k_{23}}E{N_2}(t) + ({M_3} - 2{P_4}{M_3} - {k_d})E{N_3}(t)]dt$
$dE{N_4}(t) = [{P_4}{M_3}E{N_3}(t) + ({M_4} - {k_d})E{N_4}(t)]dt$

$dEN_0^2(t) = [( - 2{k_{01}} + 2{M_0} - 2{k_d})EN_0^2(t) + 2{k_{R1}}E{N_0}{N_1}(t) + \sigma _{0,0}^2E{N_0}(t) + \sigma _{0,1}^2E{N_1}(t)]dt$
$dEN_1^2(t) = [2{k_{01}}E{N_0}{N_1}(t) + ( - 2{k_{12}} - 2{k_{R1}} - 2{k_d})EN_1^2(t) + 2{k_{R2}}E{N_1}{N_2}(t) + \sigma _{1,1}^2E{N_1}(t) + \sigma _{1,0}^2E{N_0}(t) + \sigma _{1,2}^2E{N_2}(t)]dt$
$dEN_2^2(t) = [2{k_{12}}E{N_1}{N_2}(t) + ( - 2{k_{23}} - 2{k_{R2}} - 2{k_d})EN_2^2(t) + \sigma _{2,1}^2E{N_2}(t) + \sigma _{2,0}^2E{N_1}(t)]dt$
$dEN_3^2(t) = [2{k_{23}}E{N_2}{N_3}(t) + (2{M_3} - 4{P_4}{M_3} - 2{k_d})EN_3^2(t) + \sigma _{3,1}^2E{N_3}(t) + \sigma _{3,0}^2E{N_2}(t)]dt$
$dEN_4^2(t) = [2{P_4}{M_3}E{N_3}{N_4}(t) + (2{M_4} - 2{k_d})EN_4^2(t) + \sigma _{4,1}^2E{N_4}(t) + \sigma _{4,0}^2E{N_3}(t)]dt $

$dE{N_0}{N_1}(t) = [{k_{01}}EN_0^2(t) + {k_{R1}}EN_1^2(t) + ({M_0} - {k_{01}} - {k_{12}} - {k_{R1}} - 2{k_d})E{N_0}{N_1}(t) + {k_{R1}}E{N_0}{N_2}(t)]dt$
$dE{N_0}{N_2}(t) = [({M_0} - {k_{01}} - {k_{23}} - {k_{R2}} - 2{k_d})E{N_0}{N_2}(t) + {k_{R1}}E{N_1}{N_2}(t) + {k_{12}}E{N_0}{N_1}(t)]dt$
$dE{N_1}{N_2}(t) = [{k_{01}}E{N_0}{N_2}(t) + {k_{12}}EN_1^2(t) + {k_{R2}}EN_2^2(t) + ( - {k_{12}} - {k_{23}} - {k_{R1}} - {k_{R2}} - 2{k_d})E{N_1}{N_2}(t)]dt$
$dE{N_2}{N_3}(t) = [{k_{23}}EN_2^2(t) + {k_{12}}E{N_1}{N_3}(t) + ({M_3} - 2{P_4}{M_3} - {k_{23}} - {k_{R2}} - 2{k_d})E{N_2}{N_3}(t)]dt$
$dE{N_1}{N_3}(t) = [{k_{01}}E{N_0}{N_3}(t) + {k_{23}}E{N_1}{N_2}(t) + {k_{R2}}E{N_2}{N_3}(t) + ( - {k_{12}} - {k_{R1}} + {M_3} - 2{P_4}{M_3} - 2{k_d})E{N_1}{N_3}(t)]dt$
$dE{N_0}{N_3}(t) = [{k_{R1}}E{N_1}{N_3}(t) + {k_{23}}E{N_0}{N_2}(t) + ({M_0} + {M_3} - 2{P_4}{M_3} - {k_{01}} - 2{k_d})E{N_0}{N_3}(t)]dt$
$dE{N_3}{N_4}(t) = [{k_{23}}E{N_2}{N_4}(t) + {P_4}{M_3}EN_3^2(t) + ({M_3} - 2{P_4}{M_3} + {M_4} - 2{k_d})E{N_3}{N_4}(t)]dt$
$dE{N_2}{N_4}(t) = [{k_{12}}E{N_1}{N_4}(t) + {P_4}{M_3}E{N_2}{N_3}(t) + ({M_4} - {k_{23}} - {k_{R2}} - 2{k_d})E{N_2}{N_4}(t)]dt$
$dE{N_1}{N_4}(t) = [{k_{01}}E{N_0}{N_4}(t) + {k_{R2}}E{N_2}{N_4}(t) + {P_4}{M_3}E{N_1}{N_3}(t) + ({M_4} - {k_{12}} - {k_{R1}} - 2{k_d})E{N_1}{N_4}(t)]dt$
$dE{N_0}{N_4}(t) = [{k_{R1}}E{N_1}{N_4}(t) + {P_4}{M_3}E{N_0}{N_3}(t) + ({M_0} + {M_4} - {k_{01}} - 2{k_d})E{N_0}{N_4}(t)]dt$

Поясните пожалуйста правильно ли я действую и похожи ли такие результаты на правду?...

[Alexey1]

Напишите подробнее что Вы делаете. Каким образом Вы используете формулу Ито? Что означают все обозначения, где детерминированные функции, а где случайные процессы?