1192 JOURNAL.OF POLITICAL ECONOMY and the surprise terms can be represented as mutually independent Wiener processes: dw"=-(ds"-fdt), 0 dWg=二(ds“-0, 0 dw=三(dD-0. Op These processes are a standard three-dimensional Brownian motion only for agents in group B. Since the beliefs of all agents have constant variance,we shall refer to the conditional mean of the beliefs as their beliefs.We let ga and g"denote the differences in beliefs: g1=-,g"=1- The next proposition describes the evolution of these differences in beliefs. PROPOSITION 1. dg=-pg'dt+odw., where +o+0-(层+》 0=200, and wa is a standard Wicner process for agents in group A,with in- novations that are orthogonal to the innovations of f. Proposition 1 implies that the difference in beliefs g*follows a simple mean-reverting diffusion process in the mind of group A agents.In particular,the volatility of the difference in beliefs is zero in the absence of overconfidence.A larger leads to greater volatility.In addition, -p/202 measures the pull toward the origin.A simple calculation shows that this mean reversion"decreases with o.A higher causes an increase in fluctuations of opinions and a slower mean reversion. In an analogous fashion,for agents in group B,gasatisfies dg"=一pgh+oW, "Conley et al.(1997)arguc that this is the correct measure of mean reversion. Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission