Accuracy of numerical solutions using the eulers equation residuals

In this paper we derive sorne asymptotic properties on the accuracy of numerical solutions. We sIlow tIlat the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error tIle most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests that can assess the performance of alternative computational methods

On the policy function in continuos time economic models

In this paper, I consider a general class of continuous-time economic models with unbounded horizon. I study the sets of conditions under which the policy function is continuous, Lipschitz continuous, and Cl differentiable. 1 also single out certain postulates which may prevent higher-order differentiability. The analysis provides, therefore, a fmn foundation to the use of dynamic programming methods in continuous time models with unbounded horizo

Consistency properties of a simulation-based estimator for dynamic processes

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the uniform convergence (a.s.) of a family of sample distributions over the domain of parameters. This uniform convergence holds under mild continuity and monotonicity conditions on the dynamic process. The estimator is applied to an asset pricing model with technology adoption. A challenge for this model is to generate the observed high volatility of stock markets along with the much lower volatility of other real economic aggregates.Comment: Published in at http://dx.doi.org/10.1214/09-AAP608 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

High contrast optical modulation by surface acoustic waves

Numerical Calculations are employed to study the modulation of light by surface acoustic waves (SAWs) in photonic band gap (PBG) structures. The on/off contrast ratio in PBG switch based on optical cavity is determined as a function of the SAW induced dielectric modulation. We show that these structures exhibit high contrast ratios even for moderate acousto-optic couplingComment: 7 manuscript pages and 5 figures; submitted to Applied Physics Letters on April 24, 200

The relevance of random choice in tests of Bell inequalities with atomic qubits

It is pointed out that a loophole exists in experimental tests of Bell inequality using atomic qubits, due to possible errors in the rotation angles of the atomic states. A sufficient condition is derived for closing the loophole