I don't have a specific problem I need an answer for. I have a curiosity on how to find the conditional probability of a stochastic process.
Let's say the random process $X(t)$ is wide sense stationary Gaussian with mean and variance as known parameters. How would one calculate the probability $\mathbb{P}( X(t_1) < x | X_t=y )$?.
I cannot seem to find anything out there to answer this question.