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.

Analysis of low density codes and improved designs using irregular graphs

Abstract: We introduce a new set of probabilistic analysis tools based on the analysis of And-Or trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, includingrandom loss-resilient codes, solving random k-SAT formula using the pure literal rule, and thegreedy algorithm for matchings in random graphs. In addition, these tools allow generalizations of these problems not previously analyzed to be analyzed in a straightforward manner. We illustrate our methodology on the three problems listed above

Bayesian design and analysis of computer experiments: Use of derivatives in surface prediction

Abstract: This article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain T, given values of yo and all of its first derivatives at a set of design sites (points) in T. The intended application is to computer experiments in which yo is an output from a computer model of a physical system and each point in T represents a particular configuration of the input parameters. It is assumed that the first derivatives are already available (e.g., from a sensitivity analysis) or can be produced by the code that implements the model. A Bayesian approach in which the random function that represents prior uncertainty about yo is taken to be a stationary Gaussian stochastic process is used. The calculations needed to update the prior given observations of yo and its first derivatives at the design sites are given and are illustrated in a small example. The issue of experimental design is also discussed, in particular the criterion of maximizing the reduction in entropy...

Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps

Abstract: We consider a stochastic process driven by diffusions and jumps Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred This allows us to determine a consistent non-parametric estimator of the integrated volatility when the infinite activity jump component is Levy Jump size estimation and central limit results are proved in the case of finite activity jumps Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data

Polynomial Chaos in Stochastic Finite Elements

Abstract: A new method for the solution of problems involving material variability is proposed. The material property is modeled as a stochastic process. The method makes use of a convergent orthogonal expansion of the process. The solution process is viewed as an element in the Hilbert space of random functions, in which a sequence of projection operators is identified as the polynomial chaos of consecutive orders. Thus, the solution process is represented by its projections onto the spaces spanned by these polynomials