Maxentropic Reconstruction of Some Probability Distributions

We propose a variational method to describe some families of probability distributions. The given probability distributions are to be found from the knowledge of the expected values of some variables. To do that we restate the problem as a constrained linear inverse problem, which we then proceed to solve by the method of maximum entropy on the mean.     

Bounds for the First eigenvalue of a spherical cap

We study upper and lower bounds for the lowest eigenvalueλ of the Laplace operator on a spherical capC _θ inm-dimensional space (m ≥ 3). We prove that these bounds are sharp by finding asymptotic expressions forλ asθ → π and asθ → 0.     

Remarks on the equation dXt = a(Xt)dBt

We prove that if a global solution of the equation dX_t = a(X_t) dB_t, X₀ = x exists for some x ? $\text{R}$ and ∫^∞₀a²(X_s)ds = ∞, then one must have a ≠ 0 a.e.