I am fairly new to stochastic calculus and am having problems solving this equation..
$$X(t)=\oint_0^TL(t)(\mu \, dt + \sigma \, dW_t)$$
Now, here $L(t)$ is a constant $k$.
And I have to find $X(t)$ in terms of $WT,k,σ,μ$.
How to proceed doing this?
I only know how to solve the first part which would be $kμT$. But, what about the second part which is a weiner process? Should it be simply $σWT$ as well?
Any help will be much appreciated!
yes, you are correct since
$$\int_0^T\sigma dW_t=\sigma\int_0^T dW_t=\sigma(W_T-W_0)=\sigma W_T$$