Find a univariate slice distribution of a PoissonProcess:

Find a bivariate slice distribution of a WienerProcess:

Find a multivariate slice distribution of a moving-average time series:

It does not autoevaluate but behaves like a distribution:

Slice distribution behaves like a distribution:

Probability density function:

Characteristic function:

Moments:

Generate a set of pseudorandom numbers:

Slice distribution may autoevaluate to known distributions:

Slice distribution for an M/M/ queue:

Probability density function:

Cumulative distribution function:

Mean of the slice distribution:

Find the limit of the mean as t approaches :

This agrees with the mean of the corresponding StationaryDistribution:

As well as the mean system size in the steady state:

Slice distribution at infinity is StationaryDistribution:

Use implicit times for computing probabilities:

Obtain the same result using the slice distribution:

Compute an expectation using implicit time in the variable x[t]:

Obtain the same result using the slice distribution:

For some continuous-time random processes, simulation of a slice distribution is not well defined:

The process path simulation between the origin and the end time depends on the choice of step:

The slice distribution simulations for a few step choices show the approximations of the exact slice distribution: