Stochastic dynamic analysis of a Kaplan turbine system considering synergistic regulation

A stochastic dynamic model of a Kaplan turbine is established in this paper during the transient process. When the Kaplan turbine operates with fluctuating load, the synergistic relationship between the guide vanes and blades experiences random fluctuation resulting from the mechanical, hydraulic and signal factors. To study the effect of stochastic fluctuations of the synergistic relationship, Chebyshev polynomial approximation method is adopted to analyze the stochastic dynamic characteristics of the Kaplan turbine during the transient process. Using Chebyshev polynomial approximation, the stochastic model of the Kaplan turbine is simplified to its equivalent deterministic model, and the stochastic dynamic characteristics of the model are investigated in the transient process. The effects of stochastic intensity on the dynamic behaviors of the Kaplan turbine are analyzed by means of numerical simulation. Moreover, the influences of PID parameters on the stochastic dynamic characteristics of the Kaplan turbine are studied through bifurcation diagrams. Analysis of stochastic characteristics and dynamic behaviors suggests that transient performance improvement can be obtained by controlling the synergistic stochastic intensity and PID parameters.

Measuring Discrepancies Between Poisson and Exponential Hawkes Processes

Poisson processes are widely used to model the occurrence of similar and independent events. However they turn out to be an inadequate tool to describe a sequence of (possibly differently) interacting events. Many phenomena can be modelled instead by Hawkes processes. In this paper we aim at quantifying how much a Hawkes process departs from a Poisson one with respect to different aspects, namely, the behaviour of the stochastic intensity at jump times, the cumulative intensity and the interarrival times distribution. We show how the behaviour of Hawkes processes with respect to these three aspects may be very irregular. Therefore, we believe that developing a single measure describing them is not efficient, and that, instead, the departure from a Poisson process with respect to any different aspect should be separately quantified, by means of as many different measures. Key to defining these measures will be the stochastic intensity and the integrated intensity of a Hawkes process, whose properties are therefore analysed before introducing the measures. Such quantities can be also used to detect mistakes in parameters estimation.

Option Pricing under Double Stochastic Volatility Model with Stochastic Interest Rates and Double Exponential Jumps with Stochastic Intensity

We present option pricing under the double stochastic volatility model with stochastic interest rates and double exponential jumps with stochastic intensity in this article. We make two contributions based on the existing literature. First, we add double stochastic volatility to the option pricing model combining stochastic interest rates and jumps with stochastic intensity, and we are the first to fill this gap. Second, the stochastic interest rate process is presented in the Hull–White model. Some authors have concentrated on hybrid models based on various asset classes in recent years. Therefore, we build a multifactor model with the term structure of stochastic interest rates. We also approximated the pricing formula for European call options by applying the COS method and fast Fourier transform (FFT). Numerical results display that FFT and the COS method are much faster than the numerical integration approach used for obtaining the semi-closed form prices. The COS method shows higher accuracy, efficiency, and stability than FFT. Therefore, we use the COS method to investigate the impact of the parameters in the stochastic jump intensity process and the existence of the process on the call option prices. We also use it to examine the impact of the parameters in the interest rate process on the call option prices.

Active-modulated, random-illumination, super-resolution optical fluctuation imaging

Super-resolution optical fluctuation imaging (SOFI) provides subdiffraction resolution based on the analysis of temporal stochastic intensity fluctuations.