Question: the probability of Gaussian process increments

Question

I have a question about increments of Gaussian process.

I think I am confused with the concept if Random variable and process.. :-(

Could I express a only one expression below the probability?

Assuming X(t) is Gaussian process with stationary increment, not independent increment.

Y(t) is the process from the increment of X(t).

Y(t) = {X(1)-X(0), X(2)-X(1), X(3)-X(2), ... }
     = {Y(0), Y(1), Y(2), ...}

Then, the elements of Y(t) is Gaussian random variable with correlation.

Assuming each variable of Y(t) is following standard normal distribution.

How can I express the probability that the samples from the process is larger than constant number c over the entire process Y(t)?

I want to say it over the entire process, not over the specific time slot.

I think P(Y(t) > c) is incorrect

and P(Y(1) > c) is also incorrect, I think.

I agonized with this problem for a week but I cannot solve it..

Please give me a little help!!