Open main menu

In probability theory, a telescoping Markov chain (TMC) is a vector-valued stochastic process that satisfies a Markov property and admits a hierarchical format through a network of transition matrices with cascading dependence.

For any consider the set of spaces . The hierarchical process defined in the product-space

is said to be a TMC if there is a set of transition probability kernels such that

  1. is a Markov chain with transition probability matrix
  2. there is a cascading dependence in every level of the hierarchy,
        for all
  3. satisfies a Markov property with a transition kernel that can be written in terms of the 's,
where and