Phase-Type Distributions and Optimal Stopping for Autoregressive Processes

Selecting Optimal Multistep Predictors for Autoregressive Processes

We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregres-sive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct predictors) can be obtained from this model. We ...

Optimal Stopping Problems for Some Markov Processes

In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93–108] and [Teor. Veroyatn. Primen. 45 (2000) 657–669] and Irles and Pa...

Optimal Stopping Games for Markov Processes

where the horizon T (the upper bound for τ and σ above) may be either finite or infinite (it is assumed that G1(XT ) = G2(XT ) if T is finite and lim inft→∞G2(Xt) ≤ lim supt→∞G1(Xt) if T is infinite). If X is right-continuous, then the Stackelberg equilibrium holds, in the sense that V ∗(x) = V∗(x) for all x with V := V ∗ = V∗ defining a measurable function. If X is right-continuous and left-co...

Optimal Stopping Rules for Directionally Reinforced Processes

Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions

Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...