Abstract

Citation

Researchers should cite this work as follows:

• Brian Winkel (2024). 1-027-StochasticProcesses-ModelingScenario. SIMIODE, (Version 3.0). QUBES Educational Resources. doi:10.25334/BA33-M747

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Article Context

Description

Fasten your seat belts! We are going to take a fascinating journey into the world of random events and modeling uncertainty in which we will build a system of an infinite (yes you read that right!) number of differential equations to model random or stochastic events. We will use straightforward differential equations techniques to solve any and all differential equations that come our way in this study. We will apply this approach to model a number of practical phenomena.

These equations are studied and modeled in more detail in a very applied field called operations research. The method of our madness is to engage you in your own discovery and march on for results. If you truly engage, ask questions, address issues we raise, then you will benefit. Otherwise, you will have done nothing more than read through stuff to the end and seen formulae which can be obtained in a much easier manner, e.g., look it up in some technical manual or formula set in a standard textbook in stochastic processes. So the journey will be a rich one, filled with amazing twists and turns. Get your supplies together for the trip.

We shall take a journey into some basic probability notions, but firmly guide you through these introductory notions in context of building differential equations models.

Basically, we are going to introduce you to a modeling tool to help you understand the notion of randomness and that tool is called a stochastic process. Then we will apply it to see if real phenomena are random by analyzing some real data.