Check exact lumpability of a Markov chain

Verifies the strong lumpability condition with respect to a partition of the state space. For every pair of macro-states, all micro-states in the same source macro-state must have the same total probability of moving to the destination macro-state.

Usage

is.lumpable(object, partition, tol = 1e-10)

# S4 method for class 'markovchain'
is.lumpable(object, partition, tol = 1e-10)

Arguments

object

A markovchain object.

partition

A named list of character vectors defining macro-states.

tol

Non-negative numerical tolerance for equality checks.

Value

A logical value.

References

Kemeny, J. G. and Snell, J. L. (1960). Finite Markov Chains.