I need to solve this system of stochastic differential equations:
$$\begin{cases}
dX_1(t)=dt+dW_1(t), \\[2ex]
dX_2(t)=X_1(t)dW_2(t),
\end{cases}$$
where $W_1(t), W_2(t)$ are independent Wiener processes.
From the first equation I found:
$$X_1(t) = t + W_1(t)$$
Then, I substituted $X_1(t)$ in the second equation:
$$dX_2(t)=(t+W_1(t))dW_2(t)=tdW_2+W_1(t)dW_2(t)$$
And I'm stuck on this step. I will be grateful for any help.
2026-03-29 03:23:11.1774754591
Find solution of stochastic differential equations
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