Many systems in the real world are periodic due to phenomena nature. Periodic hybrid stochastic differential equations often used model them. In many situations, it is inappropriate study whether solutions of will converge an equilibrium state (say, 0 or trivial solution) but more appropriate discuss probability distributions a stationary distribution, known as stability distribution. This pape...

In condition monitoring a part of the information necessary for decision-making comes from scrutinizing a time measure or a transform of this measure. Frequency domain is commonly exploited; lag domain is not, albeit advantages of the autocorrelation function have long been known. In this paper, we dwell on the autocorrelation function in order to extract some interesting properties of the meas...

We present analytic results for the current in a system moving in an arbitrary periodic potential and driven by weak Gaussian noise with an arbitrary power spectrum which are valid to order (tc/tr) , where tc is the largest characteristic time of the noise, and tr is the characteristic intrawell relaxation time. The dependence of the current on the shape of the potential, and on the shape of th...

Noise is widely understood to be something that interferes with a signal or process. Thus, it is generally thought to be destructive, obscuring signals and interfering with function. However, early in the 20th century, mechanical engineers found that mechanisms inducing additional vibration in mechanical systems could prevent sticking and hysteresis. This so-called “dither” noise was later intr...