New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme molecules behave fundamentally differently from what classical model predicts. A stochastic network model was previously proposed to explain the experimental disco...

Preface We introduce parameters called normalized mean square covariance (NMSV), normalized mean square correlation (NMSR), re-centered normalized mean square correlation (RC-NMSR), and stochastic degree of freedom (SDF) to efficiently characterize the correlation properties of Ä ¾ stochastic processes. We show that these parameters are very useful to characterize wireless communication channel...

We address a question on the effect of common stochastic inputs on the correlation of the spike trains of two neurons when they are coupled through direct connections. We show that the change in the correlation of small amplitude stochastic inputs can be better detected when the neurons are connected by direct excitatory couplings. Depending on whether intrinsic firing rate of the neurons is id...

In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect to the possible choice of correlation. Thus, it becomes a ...

We address a question on the effect of common stochastic inputs on the correlation of the spikes trains of two neurons when they are possibly nonidentical and are coupled through direct connections. We show that the change in the correlation of low amplitude stochastic inputs can be better detected when the neurons are connected by direct excitatory couplings. Depending on whether the neurons a...

A new class of stochastic covariance models based on Wishart distribution is proposed. Three categories of dynamic correlation models are introduced depending on how the timevarying covariance matrix is formulated and whether or not it is a latent variable. A stochastic covariance filter is also developed for filtering and predicting covariances. Extensions of the basic models enable the study ...

The phase space for Hamiltonians of two degrees of freedom is usually divided into stochastic and integrable components. Even when well into the stochastic regime, integrable orbits may surround small stable regions or islands. The effect of these islands on the correlation function for the stochastic trajectories is examined. Depending on the value of the parameter describing the rotation numb...

We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...

We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...

We consider both the effect of particle inertia on stochastic Stokes’ drift, and also a related process which could be considered as a crude model of stochastic Stokes’ drift driven by an eddy diffusivity. In the latter, the stochastic forcing is a stable Ornstein–Uhlenbeck process rather than Brownian motion. We show that the eddy Stokes’ drift velocity has a peak at a non-zero value of the co...