Weak Markov processes as linear systems

Linear Additive Markov Processes

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parameterization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its stead...

A necessary condition for weak lumpability in finite Markov processes

Under certain conditions, the state space of a homogeneous Markov process can be partitionned to construct an aggregated markovian process. However, the verification of these conditions requires expensive computations. In this note, we expose a necessary condition for having a markovian aggregated process. This condition is based on properties of the eigenvalues of certain submatrices of the tr...

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

The KTH Visit in Semi-Markov Processes

Weak Approximation for Linear Systems of Quadrics

We give local conditions at ∞ ensuring that the intersection of n quadrics in P , N ≫ n, satisfies weak approximation. Let K be a number field, V a finite-dimensional vector space over K, and W ⊂ Sym V ∗ a K-vector space of quadratic forms on V . We can regard W as a linear system of quadrics in PV , and we denote the intersection of all quadrics in the system XW . If S is a finite set of place...