When a stochastic process would be a beneficial model in terms of noise

1. What is white noise in stochastic processes?
2. What are stochastic processes used for?
3. What are all the four types of stochastic process?
4. What is a stochastic process provide an example?

What is white noise in stochastic processes?

White noise is defined as a generalized stochastic process X[u] such that for each u, the random variable X[u] is Gaussian with mean 0 and variance the integral of u-square.

What are stochastic processes used for?

Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.

What are all the four types of stochastic process?

Some basic types of stochastic processes include Markov processes, Poisson processes (such as radioactive decay), and time series, with the index variable referring to time. This indexing can be either discrete or continuous, the interest being in the nature of changes of the variables with respect to time.

What is a stochastic process provide an example?

A stochastic process is a collection or ensemble of random variables indexed by a variable t, usually representing time. For example, random membrane potential fluctuations (e.g., Figure 11.2) correspond to a collection of random variables , for each time point t.