We say Xt with paramters (µ,σ) is brownian process if (Xt-s - X t) ~N (µs,σ2 s) AMONG other conditons .
Here we don't speak about any particular distribution for X t. We only say it is a brownian motion and its increments are normally distributed.
But when it comes to standard brownian motion ( Wt) , why do we say it has a normal distribution i.e Wt ~ N(0,t).
Does that mean I can say any brownian motion process Xt with parameters is µ,σ is also normally distributed N(µt,σ2 s)?
I am new to this topic and if the question does not have a logic, please enlighten with your inputs
edit 1: it would be helpful if the explanation is more intuitive than mathematical