Foundations and Trends® in Stochastic Systems

Volume 1, issue 4

Solving Free-boundary Problems with Applications in Finance

Stochastic control problems in which there are no bounds on the rate of control reduce to so-called free-boundary problems in partial differential equations (PDEs). In a free-boundary problem the solution of the PDE and the domain over which the PDE must be solved need to be determined simultaneousl...
Volume 1, issue 3

Long Range Dependence

The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced processes, h...
Volume 1, issue 2

Controlled Markov Chains, Graphs, and Hamiltonicity

This manuscript summarizes a line of research that maps certain classical problems of discrete mathematics — such as the Hamiltonian Cycle and the Traveling Salesman Problems — into convex domains where continuum analysis can be carried out. Arguably, the inherent difficulty of these, now classical,...
Volume 1, issue 1

Monotonicity in Markov Reward and Decision Chains: Theory and Applications

This paper focuses on monotonicity results for dynamic systems that take values in the natural numbers or in more-dimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth....