Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes

Abstract: Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation models for failure based on the geometric Brownian motion or gamma process. It is shown that in most cases, our models for failure can be approximated closely by accelerated test versions of Birnbaum–Saunders and inverse Gaussian distributions. Estimation of model parameters and a model selection procedure are discussed, and two illustrative examples using real data for carbon-film resistors and fatigue crack size are presented.

Quantifying cross-correlations using local and global detrending approaches

Abstract: In order to quantify the long-range cross-correlations between two time series qualitatively, we introduce a new cross-correlations test QCC(m), where m is the number of degrees of freedom. If there are no cross-correlations between two time series, the cross-correlation test agrees well with the χ2(m) distribution. If the cross-correlations test exceeds the critical value of the χ2(m) distribution, then we say that the cross-correlations are significant. We show that if a Fourier phase-randomization procedure is carried out on a power-law cross-correlated time series, the cross-correlations test is substantially reduced compared to the case before Fourier phase randomization. We also study the effect of periodic trends on systems with power-law cross-correlations. We find that periodic trends can severely affect the quantitative analysis of long-range correlations, leading to crossovers and other spurious deviations from power laws, implying both local and global detrending approaches should be applied to properly uncover long-range power-law auto-correlations and cross-correlations in the random part of the underlying stochastic process.

Stochastic volatility : selected readings

Abstract: General Introduction PART I: MODEL BUILDING 1. A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices 2. Financial Returns Modelled by the Product of Two Stochastic Processes: A Study of Daily Sugar Prices, 1961-79 3. The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices 4. The Pricing of Options on Assets with Stochastic Volatilities 5. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model 6. Multivariate Stochastic Variance Models 7. Stochastic Autoregressive Volatility: A Framework for Volatility Modelling 8. Long Memory in Continuous-time Stochastic Volatility Models PART II: INFERENCE 9. Bayesian Analysis of Stochastic Volatility Models 10. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models 11. Estimation of Stochastic Volatility Models with Diagnostics PART III: OPTION PRICING 12. Pricing Foreign Currency Options with Stochastic Volatility 13. A Closed-Form Solution for Options with Stochastic Volatility, with Applications to Bond and Currency Options 14. A Study Towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation PART IV: REALISED VARIATION 15. The Distribution of Exchange Rate Volatility 16. Econometric Analysis of Realized Volatility and its use in Estimating Stochastic Volatility Models Index

Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials

Abstract: The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This article begins with a review of these quantities, their interpretation, and how they may be estimated. A discussion of how to assess the statistical significance of features in these measures is included. In addition, new work is presented that builds on the framework established in the review section. This work investigates how the estimates and their error bars are modified by finite sample sizes. Finite sample corrections are derived based on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low-variance gaussian process. It is found that in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale set by the number of point events in the interval. Alternatively, the degrees of freedom of the estimators can be thought of as bounded from above by the expected number of point events in the interval. Further new work describing and illustrating a method for detecting the presence of a line in a point process spectrum is also presented, corresponding to the detection of a periodic modulation of the underlying rate. This work demonstrates that a known statistical test, applicable to continuous processes, applies with little modification to point process spectra and is of utility in studying a point process driven by a continuous stimulus. Although the material discussed is of general applicability to point processes, attention will be confined to sequences of neuronal action potentials (spike trains), the motivation for this work.