Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Stochastic processes and their finite-dimensional distributions
Definition
For , let be a random element. The family is a stochastic process. For an ordered tuple of distinct times , its finite-dimensional distribution is the pushforward law of on . These laws, including their coordinate order, form a consistent family under deletion and permutation of times.
Depends on
Used by
- The canonical coordinate process realizes consistent finite-dimensional laws Corollary
- One-dimensional marginals alone do not specify a joint law Counterexample
- Process law, modification, and indistinguishability Definition
- A canonical random walk from product increments Example
- Finite-dimensional distributions determine a process law on the cylinder sigma-algebra Theorem
Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Biskup, MATH 275D notes, Definition 2.1 (standard reference, not scraped)