A Minimum Disparity Distance Estimator minimizes a φ-divergence between the marginal density of a parametric model and its non-parametric estimate. This principle is applied to the estimation of stochastic differential equation models, choosing the Hellinger distance as particular φ−divergence. Under an hypothesis of stationarity, the parametric marginal density is provided by solving the Kolmo...

This paper develops a method to rigorously show the validity of continuum description for the deterministic dynamics of many interacting particles with random initial data. We consider a hard sphere flow where particles are removed after the first collision. A fixed number of particles is drawn randomly according to an initial density f0(u, v) depending on d-dimensional position u and velocity ...

The forward di¤usion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene …xation, with the “weight”associated with the spikes corresponding to th...

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We generalize the Kolmogorov continuity theorem and prove of a class stochastic fields with parameter. As an application, we derive solutions for nonlocal parabolic equations driven by non-Gaussian Lévy noises.

Linear and nonlinear Lagrangian equations are derived for stochastic processes that appear as solutions of the averaged hydrodynamic equations, since their moments satisfy the budgets given by these equations. These equations include the potential temperature, so that non-neutral flows can be described. They will be compared with nonlinear and non-Markovian equations that are obtained using con...

We establish the existence and uniqueness, in bounded as well unbounded Lipschitz type cylinders of forms UX×VY,t Ω×Rm×R, weak solutions to Cauchy-Dirichlet problems for strongly degenerate parabolic operatorL:=∇X⋅(A(X,Y,t)∇X)+X⋅∇Y−∂t, assuming that A=A(X,Y,t)={ai,j(X,Y,t)} is a real m×m-matrix valued, measurable function such A(X,Y,t) symmetric, uniformly elliptic. Subsequently we solve contin...