Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

A modification to the OE IIR system structure is proposed to ensure global convergence for sufficient modeling of the unknown system. The proposed structure is effectively equivalent to whitening the input signal before being applied to the original OE setup. This guarantees the unimodality of the error surface for sufficient modeling. An adaptive update scheme for the new structure is derived ...

We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean can be retrieved in a blow-up limit from them. As consequence, prove the viscosity solutions to rescaled geometric flows locally uniformly converge solution motion. The result is achieved by combining compactness argument set-theoretic approach related theory of De Gi...

We consider the mean-field limit of systems particles with singular interactions type −log|x| or |x|−s, 00, is global time, it first such result valid for both conservative gradient flows setting on Rd. The proof relies adaptation ar...

We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These require step be sufficiently small, but do not strong convexity either unary or pairwise potential terms in model. To handle high dimensionality, our proof uses a particlewise coupling that is c...