TY - GEN

T1 - Coarse resistance tree methods for stochastic stability analysis

AU - Borowski, Holly

AU - Marden, Jason R.

AU - Leslie, David S.

AU - Frew, Eric W.

PY - 2013

Y1 - 2013

N2 - Emergent behavior in natural and manmade systems can often be characterized by the limiting distribution of a class of Markov processes termed regular perturbed processes. Resistance trees have gained popularity as a computationally efficient way to characterize the support of the limiting distribution; however, there are three main limitations of this approach. First, it requires finding a minimum weight spanning tree for each state in a potentially large state space. Second, perturbations to transition probabilities must decay at an exponentially smooth rate. Lastly, the approach is shown to hold purely in the context of finite Markov chains. In this paper we seek to address these limitations by developing new tools for characterizing the limiting distribution. First, we provide necessary conditions for stochastic stability via a coarse, and less computationally intensive, state space analysis. Next, we identify necessary conditions for stochastic stability when smooth convergence requirements are relaxed. Finally, we establish similar tools for stochastic stability analysis in Markov chains over a continuous state space.

AB - Emergent behavior in natural and manmade systems can often be characterized by the limiting distribution of a class of Markov processes termed regular perturbed processes. Resistance trees have gained popularity as a computationally efficient way to characterize the support of the limiting distribution; however, there are three main limitations of this approach. First, it requires finding a minimum weight spanning tree for each state in a potentially large state space. Second, perturbations to transition probabilities must decay at an exponentially smooth rate. Lastly, the approach is shown to hold purely in the context of finite Markov chains. In this paper we seek to address these limitations by developing new tools for characterizing the limiting distribution. First, we provide necessary conditions for stochastic stability via a coarse, and less computationally intensive, state space analysis. Next, we identify necessary conditions for stochastic stability when smooth convergence requirements are relaxed. Finally, we establish similar tools for stochastic stability analysis in Markov chains over a continuous state space.

U2 - 10.1109/CDC.2013.6760153

DO - 10.1109/CDC.2013.6760153

M3 - Conference contribution/Paper

SN - 9781467357142

SP - 1860

EP - 1865

BT - Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

PB - IEEE

ER -