The Expected Hitting Time Approach to Optimal Price Adjustment Problems

2017 ◽  
Author(s):  
Yiying Cheng ◽  
Yaozhong Hu ◽  
Chihoon Lee
Keyword(s):  
Hitting Time ◽  
Price Adjustment ◽  
Optimal Price ◽  
Adjustment Problems ◽  
Expected Hitting Time

The Study on Convergence and Convergence Rate of Genetic Algorithm Based on an Absorbing Markov Chain

2012 ◽  
Vol 239-240 ◽  
pp. 1511-1515 ◽  
Author(s):  
Jing Jiang ◽  
Li Dong Meng ◽  
Xiu Mei Xu
Keyword(s):  
Genetic Algorithm ◽  
Markov Chain ◽  
Convergence Rate ◽  
Hitting Time ◽  
Sufficient Condition ◽  
First Hitting Time ◽  
Absorbing Markov Chain ◽  
Expected Hitting Time ◽  
Optimization Efficiency ◽  
Theoretical Issues

The study on convergence of GA is always one of the most important theoretical issues. This paper analyses the sufficient condition which guarantees the convergence of GA. Via analyzing the convergence rate of GA, the average computational complexity can be implied and the optimization efficiency of GA can be judged. This paper proposes the approach to calculating the first expected hitting time and analyzes the bounds of the first hitting time of concrete GA using the proposed approach.

scholarly journals Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

2008 ◽  
Vol 40 (4) ◽  
pp. 966-978
Author(s):  
Archis Ghate
Keyword(s):  
Markov Chains ◽  
Structural Properties ◽  
Long Range ◽  
World Literature ◽  
Relative Size ◽  
Small World ◽  
Hitting Time ◽  
Hitting Times ◽  
Message Delivery ◽  
Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

A defender-attacker model and algorithm for maximizing weighted expected hitting time with application to conservation planning

2017 ◽  
Vol 49 (12) ◽  
pp. 1112-1128 ◽  
Author(s):  
Jorge A. Sefair ◽  
J. Cole Smith ◽  
Miguel A. Acevedo ◽  
Robert J. Fletcher
Keyword(s):  
Conservation Planning ◽  
Hitting Time ◽  
Expected Hitting Time

scholarly journals Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

2008 ◽  
Vol 40 (04) ◽  
pp. 966-978
Author(s):  
Archis Ghate
Keyword(s):  
Markov Chains ◽  
Structural Properties ◽  
Long Range ◽  
World Literature ◽  
Relative Size ◽  
Small World ◽  
Hitting Time ◽  
Hitting Times ◽  
Message Delivery ◽  
Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

Expected Hitting Time of Double Graphs

2021 ◽  
Vol 11 (04) ◽  
pp. 472-476
Author(s):  
春雨 孙
Keyword(s):  
Hitting Time ◽  
Expected Hitting Time

Optimal price adjustment under imperfect information

1990 ◽  
Vol 34 (5) ◽  
pp. 941-952 ◽  
Author(s):  
Amit Bhaduri ◽  
Josef Falkinger
Keyword(s):  
Imperfect Information ◽  
Price Adjustment ◽  
Optimal Price

A PRICE ADJUSTMENT PROCESS IN A MODEL OF MONOPOLISTIC COMPETITION

2004 ◽  
Vol 06 (03) ◽  
pp. 417-442 ◽  
Author(s):  
JAN TUINSTRA
Keyword(s):  
Monopolistic Competition ◽  
Demand Curve ◽  
Price Adjustment ◽  
Adjustment Process ◽  
Computational Techniques ◽  
Global Dynamics ◽  
Optimal Price ◽  
Demand Structure ◽  
Price Effects ◽  
Linear Demand

We consider a price adjustment process in a model of monopolistic competition. Firms have incomplete information about the demand structure. When they set a price they observe the amount they can sell at that price and they observe the slope of the true demand curve at that price. With this information they estimate a linear demand curve. Given this estimate of the demand curve they set a new optimal price. We investigate the dynamical properties of this learning process. We find that, if the cross-price effects and the curvature of the demand curve are small, prices converge to the Bertrand-Nash equilibrium. The global dynamics of this adjustment process are analyzed by numerical simulations. By means of computational techniques and by applying results from homoclinic bifurcation theory we provide evidence for the existence of strange attractors.

Computing an expected hitting time for the 3-urn Ehrenfest model via electric networks

2017 ◽  
Vol 127 ◽  
pp. 42-48 ◽  
Author(s):  
Yung-Pin Chen ◽  
Isaac H. Goldstein ◽  
Eve D. Lathrop ◽  
Roger B. Nelsen
Keyword(s):  
Hitting Time ◽  
Electric Networks ◽  
Expected Hitting Time
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