Unlike theoretical probability, which relies on known possibilities and logical reasoning, empirical probability is grounded in real-world observations. This makes it a valuable tool for understanding ...

We consider the problem of stationary distribution function estimation at a given point by the observations of an ergodic diffusion process on the interval [0, T] as T → ∞. First we introduce a lower ...

Some general results concerning the asymptotic behavior of the value of the empirical distribution function at a random point (e.g. the sample mean) are given. These results are then used to obtain: ...