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Invariant measures

When the transfer operator has been computed for a state space discretization, we can derive an invariant measure (probability density) over the states of the system.

Documentation

# PerronFrobenius.invariantmeasure — Function.

left_eigenvector(to::AbstractTransferOperator;
        N::Int = 200,
        tolerance::Float64 = 1e-8,
        delta::Float64 = 1e-8)

Compute the invariant probability distribution from a TransferOperator.

Computing an invariant probability distribution

The distribution is taken as a left eigenvector of the transfer matrix, obtained by repeated application of the transfer operator on a randomly initialised distribution until the probability distribution converges.

Keyword arguments

  • N: the maximum number of iterations.
  • tolerance and `delta: decides when convergence is achieved.