In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The stochasticity of the gradient can be mitigated by the injection of Gaussian nois...

The SABR stochastic volatility model with β-volatility β є (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition probability density function of the mo...

Stochastic resonance (SR) has been studied experimentally in a glow discharge plasma. For the SR phenomena, it is observed that a superimposed subthreshold periodic signal can be recovered via stochastic modulations of the discharge voltage. In the present experiments, induction of SR is quantified using the absolute mean difference (AMD). Comparison of the AMD techniques with respect to cross-...

In this work, we investigate the signal transmission in a linear static system driven by correlated multiplicative and additive noises. When the input signal is periodic, we depict the stochastic resonance (SR) phenomenon by employing the signal-to-noise ratio (SNR) theory; while the input signal is aperiodic, we describe the SR phenomenon by using the input–output cross correlation theory. And...

Necessary conditions are derived for stochastic partially observed control problems when the control enters the drift coefficient and correlation between signal and observation noise is allowed. The problem is formulated as one of complete information, but instead of considering directly the equation satisfied by the unnormalized conditional density of nonlinear filtering, measure-valued decomp...

We consider an elliptic pseudo-differential equation with a highly oscillating linear potential modeled as a stationary ergodic random field. The random field is a function composed with a centered long-range correlated Gaussian process. In the limiting of vanishing correlation length, the heterogeneous solution converges to a deterministic solution obtained by averaging the random potential. W...

We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green functio...

Gravitational wave experiments will play a key role in the investigation of the frontiers of cosmology and the structure of fundamental fields at high energies, by detecting, or setting strong upper-limits to, the primordial gravitational wave background produced in the early-Universe. Here we discuss the impact of space-borne laser interferometric detectors operating in the low-frequency windo...

Figure 3: Example of phase correlation between two microphones. The peak of this function indicates the inter-channel delay. index associated with peak value of f(t). This delay estimator is computationally convenient and more robust to noise and reverberation than other approaches based on cross-correlation or adaptive ltering. In ideal conditions, the output of Equation (5) is a delta functio...

Conventional process identification techniques of a open-loop process use the cross-correlation function between historical values of the process input and of the process output. If the process is operated under a linear feedback controller, however, the cross-correlation function has no information on the process transfer function because of the linear dependency of the process input on the ou...