scholarly journals Correlation inequalities and monotonicity properties of the Ruelle operator

2019 ◽  
Vol 19 (06) ◽  
pp. 1950048 ◽  
Author(s):  
L. Cioletti ◽  
A. O. Lopes
Keyword(s):  
Thermodynamic Formalism ◽  
Sufficient Conditions ◽  
Ising Models ◽  
Upper Bounds ◽  
Maximal Eigenvalue ◽  
Correlation Inequality ◽  
Ruelle Operator ◽  
Fkg Inequality ◽  
Power Law Decay ◽  
The Fkg Inequality

In this paper, we provide sufficient conditions for the validity of the FKG Inequality, on Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle operator. We use this correlation inequality to study the maximal eigenvalue problem for the Ruelle operator associated to low regular potentials. As an application, we obtain explicit upper bounds for the main eigenvalue (consequently, for the pressure) of the Ruelle operator associated to Ising models with a power law decay interaction energy.

scholarly journals Negative Dependence Through the FKG Inequality

1996 ◽  
Vol 3 (27) ◽  
Author(s):  
Devdatt P. Dubhashi ◽  
Volker Priebe ◽  
Desh Ranjan
Keyword(s):  
Random Variables ◽  
Negative Association ◽  
Negative Dependence ◽  
Correlation Inequality ◽  
General Technique ◽  
Fkg Inequality ◽  
Binary Random Variables ◽  
The Fkg Inequality ◽  
Occupancy Problems ◽  
Special Case

We investigate random variables arising in occupancy problems, and show the variables to be negatively associated, that is, negatively dependent in a strong sense. Our proofs are based on the FKG correlation inequality, and they suggest a useful, general technique for proving negative dependence among random variables. We also show that in the special case of two binary random variables, the notions of negative correlation and negative association coincide.

scholarly journals Ruelle operator theorem for non-expansive systems

2009 ◽  
Vol 30 (2) ◽  
pp. 469-487 ◽  
Author(s):  
YUNPING JIANG ◽  
YUAN-LING YE
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Iterated Function Systems ◽  
Ruelle Operator ◽  
Iterated Function

AbstractThe Ruelle operator theorem has been studied extensively both in dynamical systems and iterated function systems. In this paper we study the Ruelle operator theorem for non-expansive systems. Our theorems give some sufficient conditions for the Ruelle operator theorem to be held for a non-expansive system.

scholarly journals Two-Machine Job-Shop Scheduling Problem to Minimize the Makespan with Uncertain Job Durations

Algorithms ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 4 ◽  
Author(s):  
Yuri N. Sotskov ◽  
Natalja M. Matsveichuk ◽  
Vadzim D. Hatsura
Keyword(s):  
Relative Error ◽  
Job Shop ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Maximum Relative Error ◽  
Scheduling Problems ◽  
Lower And Upper Bounds ◽  
Shop Scheduling ◽  
Job Duration ◽  
On Line

We study two-machine shop-scheduling problems provided that lower and upper bounds on durations of n jobs are given before scheduling. An exact value of the job duration remains unknown until completing the job. The objective is to minimize the makespan (schedule length). We address the issue of how to best execute a schedule if the job duration may take any real value from the given segment. Scheduling decisions may consist of two phases: an off-line phase and an on-line phase. Using information on the lower and upper bounds for each job duration available at the off-line phase, a scheduler can determine a minimal dominant set of schedules (DS) based on sufficient conditions for schedule domination. The DS optimally covers all possible realizations (scenarios) of the uncertain job durations in the sense that, for each possible scenario, there exists at least one schedule in the DS which is optimal. The DS enables a scheduler to quickly make an on-line scheduling decision whenever additional information on completing jobs is available. A scheduler can choose a schedule which is optimal for the most possible scenarios. We developed algorithms for testing a set of conditions for a schedule dominance. These algorithms are polynomial in the number of jobs. Their time complexity does not exceed O ( n 2 ) . Computational experiments have shown the effectiveness of the developed algorithms. If there were no more than 600 jobs, then all 1000 instances in each tested series were solved in one second at most. An instance with 10,000 jobs was solved in 0.4 s on average. The most instances from nine tested classes were optimally solved. If the maximum relative error of the job duration was not greater than 20 % , then more than 80 % of the tested instances were optimally solved. If the maximum relative error was equal to 50 % , then 45 % of the tested instances from the nine classes were optimally solved.

scholarly journals LRU is better than FIFO under the independent reference model

1992 ◽  
Vol 29 (01) ◽  
pp. 239-243 ◽  
Author(s):  
J. van den Berg ◽  
A. Gandolfi
Keyword(s):  
Reference Model ◽  
Storage System ◽  
Replacement Strategy ◽  
Fkg Inequality ◽  
The Fkg Inequality ◽  
First In First Out ◽  
System Operating ◽  
Better Than

Consider a two-level storage system operating with the least recently used (LRU) or the first-in, first-out (FIFO) replacement strategy. Accesses to the main storage are described by the independent reference model (IRM). Using the FKG inequality, we prove that the miss ratio for LRU is smaller than or equal to the miss ratio for FIFO.

scholarly journals Dissipative conformal measures on locally compact spaces

2014 ◽  
Vol 36 (2) ◽  
pp. 649-670 ◽  
Author(s):  
KLAUS THOMSEN
Keyword(s):  
Operator Algebras ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Ruelle Operator ◽  
Conformal Measures ◽  
Continuous Potential ◽  
The One ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

SMOOTH UPPER BOUNDS FOR THE PRICE FUNCTION OF AMERICAN STYLE OPTIONS

2018 ◽  
Vol 21 (01) ◽  
pp. 1850009 ◽  
Author(s):  
LOUIS BHIM ◽  
REIICHIRO KAWAI
Keyword(s):  
Sufficient Conditions ◽  
Sample Path ◽  
Statistical Error ◽  
Upper Bounds ◽  
State Variables ◽  
Price Function ◽  
Polynomial Coefficients ◽  
Volatility Models ◽  
Piecewise Polynomial Functions ◽  
American Style

We introduce a new approach for systematically obtaining smooth deterministic upper bounds for the price function of American style options. These bounding functions are characterized by sufficient conditions, under which the bounds may be infimized. In a single implementation, the proposed approach obtains explicit bounds in the form of piecewise polynomial functions, which bound the price function from above over the whole problem domain both in time and state. As a consequence, these global bounds store a continuum of information in the form of a finite number of polynomial coefficients. The proposed approach achieves these bounds, free from statistical error, without recourse to sample path simulation, without truncating the naturally unbounded domain that arises in this problem, and without discretizing the time and state variables. Throughout the paper, we demonstrate the effectiveness of the proposed method in obtaining tight upper bounds for American style option prices in a variety of market models and with various payoff structures, such as the multivariate Black Scholes and Heston stochastic volatility models and the American put and butterfly payoff structures. We also discuss extensions of the proposed methodology to perpetual American style options and frameworks in which the underlying asset contains jumps.

Multivariate monotone likelihood ratio and uniform conditional stochastic order

1982 ◽  
Vol 19 (3) ◽  
pp. 695-701 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Conditional Probability ◽  
Likelihood Ratio ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Total Positivity ◽  
Probability Measures ◽  
Monotone Likelihood Ratio ◽  
Fkg Inequality ◽  
The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn. Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

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