stochastic

Examples of stochastic in the following topics:

• Chance Processes

  • A stochastic process is a collection of random variables that is often used to represent the evolution of some random value over time.
  • Another basic type of a stochastic process is a random field, whose domain is a region of space.
  • In other words, a stochastic process is a random function whose arguments are drawn from a range of continuously changing values.
  • Thus, the random walk serves as a fundamental model for recorded stochastic activity.
  • Summarize the stochastic process and state its relationship to random walks.

• Chance Models

  • "Stochastic" means being or having a random variable.
  • In order to understand stochastic modeling, consider the example of an insurance company projecting potential claims.
  • A stochastic model would be able to assess this latter quantity with simulations.
  • Stochastic models can be simulated to assess the percentiles of the aggregated distributions.
  • Truncating and censoring of data can also be estimated using stochastic models.

• Optimization

  • Asset prices are also modeled using optimization theory, though the underlying mathematics relies on optimizing stochastic processes rather than on static optimization.
  • Operations research also uses stochastic modeling and simulation to support improved decision-making.
  • Increasingly, operations research uses stochastic programming to model dynamic decisions that adapt to events; such problems can be solved with large-scale optimization and stochastic optimization methods.

• Biological Effects of Radiation

  • Some effects of ionizing radiation on human health are stochastic, meaning that their probability of occurrence increases with dose, while the severity is independent of dose.
  • Radiation-induced cancer, teratogenesis, cognitive decline, and heart disease are all examples of stochastic effects.
  • Deterministic effects are not necessarily more or less serious than stochastic effects; either can ultimately lead to damage ranging from a temporary nuisance to death.
  • Quantitative data on the effects of ionizing radiation on human health are relatively limited compared to other medical conditions because of the low number of cases to date and because of the stochastic nature of some of the effects.
  • Stochastic effects can only be measured through large epidemiological studies in which enough data have been collected to remove confounding factors such as smoking habits and other lifestyle factors.

• Functions of Several Variables

  • Non-deterministic, or stochastic, systems can be studied using a different kind of mathematics, such as stochastic calculus.

• Summary

  • Second, we have increasingly come to realize that the relations we see among actors in a network at a point in time are best seen as probabilistic ("stochastic") outcomes of underlying processes of evolution of networks, and probabilistic actions of actors embedded in those networks.

• Increased Cancer Risk from Radiation

  • Cancer is a stochastic effect of radiation, meaning that the probability of occurrence increases with effective radiation dose, but the severity of the cancer is independent of dose.

• Oligotrophs

  • The Caulobacter cell cycle control system has been exquisitely optimized by evolutionary selection as a total system for robust operation in the face of internal stochastic noise and environmental uncertainty.

• Introduction: Applying statistical tools to network data

  • Statistics provide useful tools for summarizing large amounts of information, and for treating observations as stochastic, rather than deterministic outcomes of social processes.

• Selective Breeding

  • Evolution may be observed in the laboratory as populations adapt to new environmental conditions and/or change by such stochastic processes as random genetic drift.