This work derives explicit series reversions for the solution of Calder\'on's problem. The governing elliptic partial differential equation is $\nabla\cdot(A\nabla u)=0$ in a bounded Lipschitz domain and with matrix-valued coefficient. corresponding forward map sends $A$ to projected version local Neumann-to-Dirichlet operator, allowing use boundary data finitely many measurements. It first sho...

Do laboratory subjects correctly perceive the dynamics of a mean-reverting time series? In our experiment, subjects receive historical data and make forecasts at different horizons. The time series process that we use features short-run momentum and long-run partial mean reversion. Half of the subjects see a version of this process in which the momentum and partial mean reversion unfold over 10...

We introduce a class of stochastic volatility models (Xt)t≥0 for which the absolute moments of the increments exhibit anomalous scaling: E (|Xt+h −Xt|) scales as hq/2 for q < q∗, but as hA(q) with A(q) < q/2 for q > q∗, for some threshold q∗. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driv...