A note on a result of Kendall
The paper deals with the optimal inspections and maintenance problem with costly information for a Markov process with positive discount factor. The associated dynamic programming equation is a quasi-variational inequality with first order differential terms. In this paper we study its different formulations: strong, visousity and evolutionary. The case of impulsive control of purely jump Markov processes is studied as a special case.
We consider integral representations of Feller probability kernels from a Tikhonov space X into a Hausdorff space Y by continuous functions from X into Y. From the existence of such a representation for every kernel it follows that the space X has to be 0-dimensional. Moreover, both types of representations coincide in the metrizable case when in addition X is compact and Y is complete. It is also proved that the representation of a single kernel is equivalent to the existence of some non-direct...
On a compact metric space X one defines a transition system to be a lower semicontinuous map . It is known that every Markov operator on C(X) induces a transition system on X and that commuting of Markov operators implies commuting of the induced transition systems. We show that even in finite spaces a pair of commuting transition systems may not be induced by commuting Markov operators. The existence of trajectories for a pair of transition systems or Markov operators is also investigated.
We consider the stochastic equation where is a one-dimensional Brownian motion, is the initial value, and is a time-dependent diffusion coefficient. While the existence of solutions is well-studied for only measurable diffusion coefficients , beyond the homogeneous case there is no general result on the uniqueness in law of the solution. The purpose of the present note is to give conditions on ensuring the existence as well as the uniqueness in law of the solution.
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.