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What is the mean and the variance of $y_t$, given the following SDE:

$dy_t = -x_t y_t dt + \sigma_1 dW^1_t$

 

$dx_t = -\sigma_2 y_t dW^2_t$

$W^1$ and $W^2$ are (possibly correlated) Wiener processes.

What is the mean and the variance of $y_t$, given the following SDE:

$dy_t = -x_t y_t dt + \sigma_1 dW^1_t$

 

$dx_t = -\sigma_2 y_t dW^2_t$

$W^1$ and $W^2$ are (possibly correlated) Wiener processes.

What is the mean and the variance of $y_t$, given the following SDE:

$dy_t = -x_t y_t dt + \sigma_1 dW^1_t$

$dx_t = -\sigma_2 y_t dW^2_t$

$W^1$ and $W^2$ are (possibly correlated) Wiener processes.

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Posch79
Posch79
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Mean and Variance of SDE

What is the mean and the variance of $y_t$, given the following SDE:

$dy_t = -x_t y_t dt + \sigma_1 dW^1_t$

$dx_t = -\sigma_2 y_t dW^2_t$

$W^1$ and $W^2$ are (possibly correlated) Wiener processes.