scholarly journals Better Runtime Guarantees via Stochastic Domination

2018 ◽  
pp. 1-17 ◽  
Author(s):  
Benjamin Doerr
Keyword(s):  
Stochastic Domination

scholarly journals Stochastic comparison of point random fields

1997 ◽  
Vol 34 (04) ◽  
pp. 868-881 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Torsten Küneth
Keyword(s):  
Point Process ◽  
Random Fields ◽  
Alternative Proof ◽  
Probability Measures ◽  
Stochastic Comparison ◽  
Sufficient Condition ◽  
Stochastic Domination ◽  
Positive Correlations ◽  
Increasing Functions

We give an alternative proof of a point-process version of the FKG–Holley–Preston inequality which provides a sufficient condition for stochastic domination of probability measures, and for positive correlations of increasing functions.

On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals

1985 ◽  
Vol 22 (04) ◽  
pp. 893-902 ◽  
Author(s):  
Hermann Thorisson
Keyword(s):  
Queue Length ◽  
Rates Of Convergence ◽  
Regenerative Process ◽  
Stochastic Domination ◽  
Homogeneous Markov Process ◽  
Ergodic Properties ◽  
Server Queue ◽  
Poisson Arrivals ◽  
Service Times ◽  
Residual Service

We consider the stable k-server queue with non-stationary Poisson arrivals and i.i.d. service times and show that the non-time-homogeneous Markov process Zt = (the queue length and residual service times at time t) can be subordinated to a stable time-homogeneous regenerative process. As an application we show that if the system starts from given conditions at time s then the distribution of Zt stabilizes (but depends on t) as s tends backwards to –∞. Also moment and stochastic domination results are established for the delay and recurrence times of the regenerative process leading to results on uniform rates of convergence.

scholarly journals An Alternative Condition for Stochastic Domination

2009 ◽  
Vol 46 (04) ◽  
pp. 1198-1200
Author(s):  
Kenshi Hosaka
Keyword(s):  
Likelihood Ratio ◽  
Stochastic Domination ◽  
Alternative Condition

We will propose an alternative condition for stochastic domination. This condition differs in an essential way from the strong likelihood ratio property. We also show an example which satisfies the new condition, but does not satisfy the strong likelihood ratio property.

A note on stochastic domination and conditional thinning

2003 ◽  
Vol 35 (4) ◽  
pp. 937-940
Author(s):  
Sandeep R. Shah
Keyword(s):  
Simulation Algorithm ◽  
Stochastic Domination ◽  
Technical Report ◽  
Biased Samples

This note investigates the simulation algorithm proposed by van Lieshout and van Zwet (2001). It is seen that this algorithm generally produces biased samples; the nature of this bias is further explored in a technical report by the author.

scholarly journals A Note on Conditioning and Stochastic Domination for Order Statistics

2008 ◽  
Vol 45 (2) ◽  
pp. 575-579 ◽  
Author(s):  
Devdatt Dubhashi ◽  
Olle Häggström
Keyword(s):  
Order Statistics ◽  
Order Statistic ◽  
Conditional Distribution ◽  
Random Variables ◽  
Stochastic Domination

For an order statistic (X1:n,…,Xn:n) of a collection of independent but not necessarily identically distributed random variables, and any i ∈ {1,…,n}, the conditional distribution of (Xi+1:n,…,Xn:n) given Xi:n > s is shown to be stochastically increasing in s. This answers a question by Hu and Xie (2006).

scholarly journals Measure change in multitype branching

2004 ◽  
Vol 36 (2) ◽  
pp. 544-581 ◽  
Author(s):  
J. D. Biggins ◽  
A. E. Kyprianou
Keyword(s):  
Branching Processes ◽  
Sufficient Conditions ◽  
Branching Random Walk ◽  
Stochastic Domination ◽  
Moment Conditions ◽  
Branching Brownian Motion ◽  
Mean Convergence ◽  
Convergence Results ◽  
Watson Process ◽  
The One

The Kesten-Stigum theorem for the one-type Galton-Watson process gives necessary and sufficient conditions for mean convergence of the martingale formed by the population size normed by its expectation. Here, the approach to this theorem pioneered by Lyons, Pemantle and Peres (1995) is extended to certain kinds of martingales defined for Galton-Watson processes with a general type space. Many examples satisfy stochastic domination conditions on the offspring distributions and suitable domination conditions combine nicely with general conditions for mean convergence to produce moment conditions, like the X log X condition of the Kesten-Stigum theorem. A general treatment of this phenomenon is given. The application of the approach to various branching processes is indicated. However, the main reason for developing the theory is to obtain martingale convergence results in a branching random walk that do not seem readily accessible with other techniques. These results, which are natural extensions of known results for martingales associated with binary branching Brownian motion, form the main application.

Stochastic domination and Markovian couplings

2000 ◽  
Vol 32 (4) ◽  
pp. 1064-1076 ◽  
Author(s):  
F. Javier López ◽  
Servet Martínez ◽  
Gerardo Sanz
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Partially Ordered ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient

For continuous-time Markov chains with semigroups P, P' taking values in a partially ordered set, such that P ≤ stP', we show the existence of an order-preserving Markovian coupling and give a way to construct it. From our proof, we also obtain the conditions of Brandt and Last for stochastic domination in terms of the associated intensity matrices. Our result is applied to get necessary and sufficient conditions for the existence of Markovian couplings between two Jackson networks.

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