The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and...

Recent studies document a decline in U.S. labor-market fluidity from as early as the 1970s on. Making use of the Annual Social and Economic supplement to the Current Population Survey, I uncover a pronounced increase in job-to-job mobility from the 1970s to the 1990s, i.e. the annual share of...

In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with memory. In our models, the waiting time involves Riemann–Liouville fractional derivative or Riemann–Liouville fractional integral....

The effects of Gaussian colored noise on time evolution of information entropy in a damped harmonic oscillator are studied in this paper. The one-dimensional non-Markovian process with Gaussian colored noise is stochastically equivalent to two-dimensional Markovian process and the dimension of...

In this work we use Feynman’s path integral formalism to show the strict equivalence between the Hamilton–Jacobi (HJ) and Fokker–Planck (FP) equations, for a Brownian harmonic oscillator characterized by a Langevin equation within the inertial regime. In this case, the Lagrangian function...

We propose a nonlinear filter to estimate the time-varying default risk from the term structure of credit default swap (CDS) spreads. Based on the numerical solution of the Fokker–Planck equation (FPE) using a meshfree interpolation method, the filter performs a joint estimation of the...

Fundamental aspects of inverse-kinetic theories for the incompressible Navier–Stokes equations [M. Tessarotto, M. Ellero, RGD24, Italy, July 10–16, 2004, AIP Conf. Proc. 762 (2005) 108; M. Ellero, M. Tessarotto, Physica A 355 (2005) 233] include the possibility of defining uniquely the kinetic...

We show, analytically and numerically, that wealth distribution in the Bouchaud–Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma...

The present paper is devoted to the numerical solution of the Fokker–Planck (FP) equation associated to the Duffing oscillator driven by colored noise. We propose an improved discretization of the standard FP operator-splitting method which renders the scheme unconditionally stable. This...