MathLiveMarkov property
For a Markov process, the probability that the process lies in a set A at a later time t, given the entire history up to time s, equals the probability given only its state at time s. It expresses that the future depends on the past only through the present state.
\mathbb{P}(X_t \in A \mid \mathcal{F}_s) = \mathbb{P}(X_t \in A \mid X_s)What the symbols mean
| state of the process at time t | |
| measurable set of states | |
| current time, with s < t | |
| later time | |
| history of the process up to time s (sigma-algebra) | |
| probability measure |
About this formula
- FieldMathematics
- TopicStochastic processes
- LevelUniversity
- Also calledMarkov process property, Markov chain property, memoryless property of stochastic process, conditional probability given present state, Markov condition, future independent of past given present
- SourceWikidata Q2221775
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