Large-deviation theory of increasing returns

Large Deviation Theory

If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a lo...

Large deviation theory and applications

Large deviation theory deals with the decay of the probability of increasingly unlikely events. It is one of the key techniques of modern probability, a role which is emphasised by the recent award of the Abel prize to S.R.S. Varadhan, one of the pioneers of the subject. The subject is intimately related to combinatorial theory and the calculus of variations. Applications of large deviation the...

Increasing Returns to Education: Theory and Evidence

We model educational investment and labor supply in a competitive economy with home and market production. Heterogeneous workers are assumed to have different productivities both at home and in the workplace. We show that there are increasing returns to education at the labor market participation margin, and that these depend directly on the elasticity of labor supply with respect to wages. Thu...

Large deviation principle in logarithmic potential theory

Large Deviation Theory for Stochastic Diierence Equations

The probability density for the solution yn of a stochastic di erence equation is considered. Following Knessl, Matkowsky, Schuss, and Tier [1] it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large deviation results for a sum of independent identically distributed random variables and for the joi...