What a model can identify
Section of Stochastic processes, part of Stochastic processes
What a model can identify
| Type | Section |
| Taught in | Stochastic processes |
| Part | Stochastic processes |
A full model specifies a joint law for the observations that the question actually uses. The calculations can be exact while the observations still fail to identify the assumptions. A short sequence of arrival counts can agree with a constant-rate Poisson process and with a process whose rate drifts slowly. The two models predict different clustering and different counts from one period to the next, so those features discriminate more sharply than a single overall average. The same gap, between a mathematical consequence and what a record can identify, returns for extinction probabilities, for stationary distributions, and for limits of maxima.
A stochastic process is the whole family \{X_t\}, not one marginal. State, clock, and independence have to be named before a theorem applies. Stationary increments fix changes over an interval of a given length. They do not freeze the distribution of the level X_t.
Used in
See also
Stochastic process · Stationary and independent increments · What a stochastic process models · State, clock, and assumptions · Toolkit for stochastic processes · Modelling checklist for a stochastic process · Markov’s inequality · Chebyshev’s inequality