Answer by pgviethung for Calculating the probability of an event defined by a...
In general, we have no implicit formula for each K. However, we can make some useful bounds. In your case, where the process is stationary, I suggest the book "Level set and extrema ..." of J.M. Azais...
View ArticleAnswer by Nate Eldredge for Calculating the probability of an event defined...
Suppose your process is continuous. (By the Kolmogorov-Centsov continuity theorem, a sufficient condition for this is that $c(s,s) + c(t,t) - 2 c(s,t) \le C |s-t|^\gamma$ for some $C, \gamma > 0$.)...
View ArticleAnswer by cardinal for Calculating the probability of an event defined by a...
I would recommend obtaining a copy of the textH. Cramer and M. R. Leadbetter (1967), Stationary and Related Stochastic Processes, John Wiley & Sons, Inc.which is available as a 2004 Dover reprint,...
View ArticleAnswer by Aldanor for Calculating the probability of an event defined by a...
Consider a standard Wiener process $W_t$ with$$W_0=0,\quad\mathbb E(W_t)=0,\quad \mathbb E(W_t\cdot W_s)=\min(t,s)$$and let $k\geq0$ be the threshold of interest.Define the first passage time...
View ArticleCalculating the probability of an event defined by a condition on a Gaussian...
Although the question itself can be expressed succinctly, I couldn't come up with a nice self-explanatory title - suggestions are welcome.Motivation/BackgroundI was investigating whether it would be...
View Article
