Properties of Stochastic Processes [closed]

1. What are the properties of stochastic process?
2. What are the 3 conditions for a stochastic process to be weakly stationary?
3. What are all the four types of stochastic process?
4. How would you classify stochastic process?

What are the properties of stochastic process?

A stochastic process is defined as a collection of random variables X=Xt:t∈T defined on a common probability space, taking values in a common set S (the state space), and indexed by a set T, often either N or [0, ∞) and thought of as time (discrete or continuous respectively) (Oliver, 2009).

What are the 3 conditions for a stochastic process to be weakly stationary?

A stochastic process Xt is weakly stationary if it meets these three conditions: The mean of the process is constant. That is, E(Xt)=μ E ( X t ) = μ (where μ is some constant) for all values of t . The second moment of Xt , or E(X2t) E ( X t 2 ) , is finite.

What are all the four types of stochastic process?

Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes.

How would you classify stochastic process?

A stochastic process is a probability model describing a collection of time-ordered random variables that represent the possible sample paths. Stochastic processes can be classified on the basis of the nature of their parameter space and state space.