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Suppose that a system is such that in a time dt, the probability that an event A occurs, given that it has not already happened, is given by:
P(t,t+dt) = w(t) * dt
The solution for the probability that A has occurred at a time t is something like:
P(t) = 1 - exp(∫0tw('t)dt')
Now suppose that w(t) is changing due to some function x such that really w(t) = w(x(t)). How do I find the probability P(x) that the event A has occurred as a function of x?
P(t,t+dt) = w(t) * dt
The solution for the probability that A has occurred at a time t is something like:
P(t) = 1 - exp(∫0tw('t)dt')
Now suppose that w(t) is changing due to some function x such that really w(t) = w(x(t)). How do I find the probability P(x) that the event A has occurred as a function of x?