Many of the readings this semester have mentioned stochastic

Many of the readings this semester have mentioned stochasticity, but this is the first reading that directly focused on it. Based on this and past readings, how would you (in your own words) define “stochasticity”? When would it be important to use stochastic models?

Solution

Sol)

In probability theory, a stochastic process, or often random process, is a collection of random variables, representing the evolution of some system of random values over time. This is the probabilistic counterpart to a deterministicprocess (or deterministic system).

Importance:

Stochastic process can be used to model the number of people or information data (computational network, p2p etc) in a queue over time where you suppose for example that the number of persons or information arrives is a poisson process.

Also in biology you have applications in evolutive ecology theory with birth-death process. In neuroscience, considering noise perturbations of ionic and chemical potential in neurons membrane.

In game theory, when you work with differential games for instance, which are a general framework for modeling many different \"real word\" problems in economy, computer science and others.

In optimisation and control of systems (stochastic control theory), were you typically model your uncertainty about the system interaction with the environment by stochastic process. Just to try to make it more concrete, automatic systems in general like for example the autopilot for cars ( you can obviously extend it for any other vehicle from mini robots to space shuttles)

In physics, more precisely in statistical physics formalisme and in complex systems.