Noise can create periodic behavior and stabilize nonlinear diffusions

Asymptotic Behavior of Nonlinear Diffusions

for a given initial data u(x, 0) = u0(x) ≥ 0, where p > 1 and N ≥ 2. Such a solution exists and it is unique in the natural weak sense under rather mild conditions on u0. In particular, this is the case for u0 ∈ L , condition which we will assume in what follows. We refer the reader to [11,10] for general results on the issues of existence, uniqueness and regularity of non-negative solutions. I...

Can Noise Create the Size and Value Effects?

Can Noise Create the Size and Value Effects? Small-capitalization and value stocks are likely to predominantly have negative noise, while large-capitalization and growth stocks are likely to have positive noise, if prices contain random noise. Negative price noise implies that small-capitalization and value stocks are more likely undervalued and thus have higher expected return than justified b...

Periodic Homogenization for Hypoelliptic Diffusions

Abstract We study the long time behavior of an Ornstein–Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation. We also derive upper bounds on the convergence rate in several ...

Bagging Can Stabilize Without Redu

Periodic solution for a delay nonlinear population equation with feedback control and periodic external source

In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides  the extension of  some previous results obtained in other studies. We give a illustrative e...