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.