I want to find the joint distribution of the random vector $(W_t, \int_0^t W_s \; \mathrm ds)$
where $W_t$ is Brownian motion. I know $W_t \sim N(0,t)$, but I don't know how to calculate the distribution of the integral
I want to find the joint distribution of the random vector $(W_t, \int_0^t W_s \; \mathrm ds)$
where $W_t$ is Brownian motion. I know $W_t \sim N(0,t)$, but I don't know how to calculate the distribution of the integral