If an n x n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper ...
Abstract: Stochastic matrices are commonly used to analyze Markov chains, but revealing them can leak sensitive information. Therefore, in this paper we introduce a technique to privatize stochastic ...
ABSTRACT: We determine the left eigenvector of a stochastic matrix M associated to the eigenvalue 1 in the commutative and the noncommutative cases. In the commutative case, we see that the ...
The stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation ...
However, we assume that we only have access to products of this matrix with vectors for each $t \in [a, b]$, so this definition will not be directly useful for ...
ABSTRACT: Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n ...
Classifying Markov chains as ergodic was more complicated than the other tasks for this calculator. The approach we took was to consider the Markov chain as an unweighted directed graph, consisting of ...
Abstract: This paper investigates injection attacks incorporating stochastic noise against linear discrete time-varying system, which is more general but also more challenging to defend than ...
An idealized clustering algorithm seeks to learn a cluster-adjacency matrix such that, if two data points belong to the same cluster, the corresponding entry would be 1; otherwise the entry would be 0 ...