We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian are pure jump Lévy processes with some ?-stable like behaviour. Included Laplace diffusion operators (??)?2, tempered nonsymmetric Finance, spectrally one-sided processes, sums subelliptic different orders. Our main results existence uniqueness classic...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

This work is devoted to stability analysis of numerical solutions for jump diffusions and jump diffusions with Markovian switching. Different from the existing treatment of Euler-Maurayama methods for solutions of stochastic differential equations, we use techniques from stochastic approximation. We analyze the almost sure exponential stability and exponential pstability. Then Markovian regime-...

The Pearson diffusions is a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. Explicit optimal martingale estimating functions are found, and the corresponding estimators are shown to be consistent and asymptotically normal. The discussion covers GMM, quasi-l...

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. Kendall shape space ̃k n through a Brownian motion on the hypersphere. This representation leads to a coordinate system for the generalized v...

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also pre...

We develop a simple model for coupling the pseudo-Goldstone bosons of QCD Or's, K's, -q) to quark fields. This nonlocal model incorporates a momentum dependent dynamical quark mass ,~ (p) in a manner consistent with global chiral symmetry. Explicit current quark masses and gauge fields are also introduced. All low energy parameters of the chiral lagrangian are expressed in terms of ~(p). In par...