scholarly journals The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks

10.3982/qe643 ◽  
2017 ◽  
Vol 8 (2) ◽  
pp. 317-365 ◽  
Author(s):  
Fedor Iskhakov ◽  
Thomas H. Jørgensen ◽  
John Rust ◽  
Bertel Schjerning
Keyword(s):  
Grid Method ◽  
Choice Models ◽  
Dynamic Choice ◽  
Continuous Dynamic ◽  
Dynamic Choice Models

Multivariate extremal processes, leader processes and dynamic choice models

1990 ◽  
Vol 22 (2) ◽  
pp. 309-331 ◽  
Author(s):  
Sidney Resnick ◽  
Rishin Roy
Keyword(s):  
Transition Probabilities ◽  
Homogeneous Case ◽  
Dynamic Choice ◽  
Underlying Distribution ◽  
Extremal Process ◽  
Time Dependent Behaviour ◽  
Stationary Transition ◽  
Dynamic Choice Models ◽  
Dependent Behaviour ◽  
Leader Process

Let (Y(t), t > 0) be a d-dimensional non-homogeneous multivariate extremal process. We suppose the ith component of Y describes time-dependent behaviour of random utilities associated with the ith choice. At time t we choose the ith alternative if the ith component of Y(t) is the largest of all the components. Let J(t) be the index of the largest component at time t so J has range {1, …, d} and call {J(t)} the leader process. Let Z(t) be the value of the largest component at time t. Then the bivariate process (J(t), Z(t)} is Markov. We discuss when J(t) and Z(t) are independent, when {J(s), 0<s≦t} and Z(t) are independent and when J(t) and {Z(s), 0<s≦t} are independent. In usual circumstances, {J(t)} is Markov and particular properties are given when the underlying distribution is max-stable. In the max-stable time-homogeneous case, {J(et)} is a stationary Markov chain with stationary transition probabilities.

Multivariate extremal processes, leader processes and dynamic choice models

1990 ◽  
Vol 22 (02) ◽  
pp. 309-331 ◽  
Author(s):  
Sidney Resnick ◽  
Rishin Roy
Keyword(s):  
Transition Probabilities ◽  
Homogeneous Case ◽  
Dynamic Choice ◽  
Underlying Distribution ◽  
Extremal Process ◽  
Time Dependent Behaviour ◽  
Stationary Transition ◽  
Dynamic Choice Models ◽  
Dependent Behaviour ◽  
Leader Process

Let ( Y (t), t &gt; 0) be a d-dimensional non-homogeneous multivariate extremal process. We suppose the ith component of Y describes time-dependent behaviour of random utilities associated with the ith choice. At time t we choose the ith alternative if the ith component of Y (t) is the largest of all the components. Let J(t) be the index of the largest component at time t so J has range {1, …, d} and call {J(t)} the leader process. Let Z(t) be the value of the largest component at time t. Then the bivariate process (J(t), Z(t)} is Markov. We discuss when J(t) and Z(t) are independent, when {J(s), 0&lt;s≦t} and Z(t) are independent and when J(t) and {Z(s), 0&lt;s≦t} are independent. In usual circumstances, {J(t)} is Markov and particular properties are given when the underlying distribution is max-stable. In the max-stable time-homogeneous case, {J(et )} is a stationary Markov chain with stationary transition probabilities.

scholarly journals HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Shu-Li Mei ◽  
De-Hai Zhu
Keyword(s):  
Boundary Effect ◽  
Grid Method ◽  
Sparse Grid ◽  
Interpolation Theory ◽  
Newton Interpolation ◽  
Dynamic Choice ◽  
Grid Approach ◽  
Sparse Grid Method ◽  
Image Edge ◽  
Grid Points

The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. Compared with the traditional multiscale numerical techniques, the proposed method is independent of the basis function. In this method, a dynamic choice scheme of external grid points is proposed to eliminate the artifacts introduced by the partitioning technique. In order to decrease the calculation amount introduced by the change of the external grid points, the Newton interpolation technique is employed instead of the traditional Lagrange interpolation operator, and the condition number of the discretized matrix different equations is taken into account of the choice of the external grid points. Using the new numerical scheme, the time complexity of the sparse grid method for the image denoising is decreased toO(4J+2j) fromO(43J), (j≪J). The experiment results show that the dynamic choice scheme of the external gird points can eliminate the boundary effect effectively and the efficiency can also be improved greatly comparing with the classical interval wavelets numerical methods.

Sign in / Sign up

Export Citation Format

Share Document