A set of tools to work with Markov Processes
Author matthieugomez
8 Stars
Updated Last
1 Year Ago
Started In
April 2019

Build status

Markov Processes

  • X = DiffusionProcess(x::AbstractVector, μ::AbstractVector, σ::AbstractVector) creates the discretized Markov Process with drift μ and volatility σ, on a grid x with reflecting boundaries.
  • generator(X) returns its associated generator (i.e. the operator f -> ∂_tE[f(x_t)|x_0=x])
  • stationary_distribution(X) returns its stationary distribution (i.e. the positive vector g such that g * generator(X) = 0)

Additive Functionals

  • M = AdditiveFunctional(X, μm, σm) creates, given a discretized Markov Process, the Additive Functional with drift μm and volatility σm
  • generator(M) returns its associated generator (i.e. the operator f -> ∂_tE[e^{m}f(x_t)|x_0=x])
  • cgf(m) returns the long run scaled CGF of m
  • tail_index(m) returns the tail index of the stationary distribution of e^m

Related Packages

  • SimpleDifferentialOperators contains more general tools to define operators with different boundary counditions. In contrast, InfinitesimalGenerators always assumes reflecting boundaries.

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