Stochastic Monotonicity and Realizable Monotonicity
نویسنده
چکیده
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of S we also present conditions on the poset A that are necessary and sufficient for equivalence. When A = S, the condition that the cover graph of S have no cycles is necessary and sufficient for equivalence. This case arises in comparing applicability of the perfect sampling algorithms of Propp and Wilson and the first author of the present paper. Short title. Stochastic and realizable monotonicity. AMS 1991 subject classifications. Primary 60E05; secondary 06A06, 60J10, 05C38.
منابع مشابه
Stochastic bounds for a single server queue with general retrial times
We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds. The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques.
متن کاملRealizableMonotonicity and Inverse Probability Transform
A system (Pα : α ∈ A) of probability measures on a common state space S indexed by another index set A can be “realized” by a system (Xα : α ∈ A) of S-valued random variables on some probability space in such a way that each Xα is distributed as Pα. Assuming that A and S are both partially ordered, we may ask when the system (Pα : α ∈ A) can be realized by a system (Xα : α ∈ A) with the monoton...
متن کاملDifferent Monotonicity Definitions in Stochastic Modelling
In this paper we discuss different monotonicity definitions applied in stochastic modelling and discuss the relationships between them. Obviously, the monotonicity concept depends on the relation order that we consider on the state space. In the case of total ordering the stochastic monotonicity used in stochasticmodelling and the realizablemonotonicity used in perfect simulation are equivalent...
متن کاملSum Formula for Maximal Abstract Monotonicity and Abstract Rockafellar’s Surjectivity Theorem
In this paper, we present an example in which the sum of two maximal abstract monotone operators is maximal. Also, we shall show that the necessary condition for Rockafellar’s surjectivity which was obtained in ([19], Theorem 4.3) can be sufficient.
متن کاملStochastic Monotonicity in Intergenerational Mobility Tables
The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. Using existing inferential procedures for testing unconditional stochastic monotonicity, we first test a set of 149 intergenerational mobility tab...
متن کامل