The optional sampling theorem for martingales indexed by a partially ordered set is true if the index set is directed. However, the corresponding result for submartingales indexed by a partially ...

We define the notion of a Markov strategy for the general optimal control problem where the index set is partially ordered. We prove that the supremum over all strategies is always attained by a ...

Causal Set Theory (CST) offers a compelling approach to reconciling quantum theory and general relativity by postulating that spacetime, at its most fundamental level, is discrete rather than ...