IndisputableMonolith.Mathematics.StochasticProcessesFromRS

   1import Mathlib
   2
   3/-!
   4# Stochastic Processes from RS — C Mathematics
   5
   6Five canonical stochastic process types (Markov chain, Brownian motion,
   7Poisson process, martingale, Gaussian process) = configDim D = 5.
   8
   9In RS: recognition fluctuations = stochastic J-cost dynamics.
  10Brownian motion = random walk in J-space.
  11Markov property: recognition at tick k+1 depends only on tick k.
  12
  13Lean: 5 process types.
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.Mathematics.StochasticProcessesFromRS
  19
  20inductive StochasticProcessType where
  21  | markovChain | brownianMotion | poissonProcess | martingale | gaussianProcess
  22  deriving DecidableEq, Repr, BEq, Fintype
  23
  24theorem stochasticProcessTypeCount : Fintype.card StochasticProcessType = 5 := by decide
  25
  26structure StochasticProcessesCert where
  27  five_types : Fintype.card StochasticProcessType = 5
  28
  29def stochasticProcessesCert : StochasticProcessesCert where
  30  five_types := stochasticProcessTypeCount
  31
  32end IndisputableMonolith.Mathematics.StochasticProcessesFromRS
  33