We consider the dynamics of systems driven by compound Poisson colored noise in the presence of inertia. We study the limit when the frictional relaxation time and the noise autocorrelation time both tend to zero. We show that the Itô and Marcus stochastic calculuses naturally arise depending on these two time scales, and an extra intermediate type occurs when the two time scales are comparable...

A receding horizon filtering problem for nonlinear continuous-time stochastic systems is considered. The paper presents the optimal receding horizon filtering equations. Derivation of the equations is based on the Kushner-Stratonovich and Fokker-Planck-Kolmogorov equations for conditional and unconditional density functions. This result could be a theoretical basis for the optimal control in no...

We consider the dynamics of systems in the presence of inertia and colored multiplicative noise. We study the limit where the particle relaxation time and the correlation time of the noise both tend to zero. We show that the limiting equation for the particle position depends on the magnitude of the particle relaxation time relative to the noise correlation time. In particular, the limiting equ...

In this article, we construct a Stratonovich solution for the stochastic wave equation in spatial dimension $$d \le 2$$ , with time-independent noise and linear term $$\sigma (u)=u$$ multiplying noise. The is spatially homogeneous its spectral measure satisfies an integrability condition which stronger than Dalang’s condition. We give probabilistic representation solution, similar to Feynman–Ka...

We recall the successes of the Hubbard-Stratonovich Transformation (HST) of many-body theory, point out its failure to cope with competing channels of collective phenomena and show how to overcome this by Variational Perturbation Theory. That yields exponentially fast converging results, thanks to the help of a variety of collective classical fields, rather than a fluctuating collective quantum...