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.

Random Walk: A Modern Introduction

Abstract: Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

STOMP: Stochastic trajectory optimization for motion planning

Abstract: We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based methods like CHOMP can get stuck in.

Structural reliability under incomplete probability information

Abstract: A comprehensive framework is set forth for the analysis of structural reliability under incomplete probability information. Under stipulated requirements of consistency, invariance, operability, and simplicity, a method is developed to incorporate in the reliability analysis incomplete probability information on random variables, including moments, bounds, marginal distributions, and partial joint distributions. The method is consistent with the philosophy of Ditlevsen’s generalized reliability index and complements existing second-moment and full-distribution structural reliability theories.

Statistical-physical models of electromagnetic interference

Abstract: Most man-made and natural electromagnetic interference, or "noise," are highly non-Gaussian random processes, whose degrading effects on system performance can be severe, particularly on most conventional systems, which are designed for optimal or near optimal performance against normal noise. In addition, the nature, origins, measurement, and prediction of the general EM interference environment are a major concern of any adequate spectral management program. Accordingly, this study is devoted to the development of analytically tractable, experimentally verifiable, statistical-physical models of such electromagnetic interference. Here, classification into three major types of noise is made: Class A (narrow band vis-a-vis the receiver), Class B (broad band vis-a-vis the receiver), and Class C (= Class A + Class B). First-order statistical models are constructed for the Class A and Class B cases. In particular, the APD (a posteriori probability distribution) or exceedance probability, PD, vis;P1 (? > ?o)A,B, (and the associated probability densities, pdf's w1(?)A,B,[1]) of the envelope are obtained; (the phase is shown to be uniformly distributed in (0, 2?). These results are canonical, i.e., their analytic forms are invariant of the particular noise source and its quantifying parameter values, levels, etc. Class A interference is described by a 3-parameter model, Class B noise by a 6-parameter model.

Stochastic-process limits : an introduction to stochastic-process limits and their application to queues

Abstract: Experiencing Statistical Regularity- Random Walks in Applications- The Framework for Stochastic-Process Limits- A Panorama of Stochastic-Process Limits- Heavy-Traffic Limits for Fluid Queues- Unmatched Jumps in the Limit Process- More Stochastic-Process Limits- Fluid Queues with On-Off Sources- Single-Server Queues- Multi-Server Queues- More on the Mathematical Framework- The Space D Useful Functions- Queueing Networks- The Spaces E and F- Appendices