Salam Mehdi and thank you for the question. My understanding is that a random process is called stochastic if we define a probability P to happen (Please check Monte Carlo techniques). For example, a chemical reaction is a stochastic process if we assume that it has a probability P to take place. This probability could therefore be compared to a random number. If the probability is higher than the random number, we assume that the reaction took place. This is one of my papers for your reference.

As far as I am concerned the term 'random' can be used to refer to a variable, and the term 'stochastic' can be used to refer to an analysis, a process or a system.

There is no difference in the basic meaning. There can be a difference in usage. Random is used to indicate no biasing or no way of knowing. Stochastic is used to describe a process. These 'definitions' are general usage. There is no rule that prohibits interchanging the usage. Indeed, random was used for both until recently. Stochastic has come into use to emphasize the process.

Thank you so much for your helpful answers.

I think ,There’s no difference between the two terms when we talk about processes.

Hello Mr,

According to explanation of A. Demir in him book, a stochastic process is a random function of time. And it is formally defined as a time-indexed family of random variables.

Stochastic is random, but within a probabilistic system. So, I agree that stochastic is related with probabilistic processes. From an stochastic process, for instance radioactivity, we can measure probabilities (such as a the decay constants is a probability of decay per unit of time). Then, also we can use this probability to predict average behaviours of large number of cases. If the process were just random, then no one probability could be measured, neither anything can be predicted. This is nature. Reciprocally, in maths if we have a random process we do not have to assume a probability within our model. But in any stochastic model we have to assume one P (at least one in the simplest case). But for short sets of data they are undistinguishable.

Hi, Although the link is focused on machine learning, I found it useful due to its broader explanation.

https://machinelearningmastery.com/stochastic-in-machine-learning/

regards

Burhan Rashid Hussein

Good Answer Haydn Barros

A variable (or process) is described as stochastic if the probabilistic nature of the variable is in attention focus (e.g., in situations that we are interested in focusing on such as a partial dependence of the next event on the current event). On the other hand, a variable (or process) is described as random if the independence of the events is more focused.

A variable is random. A process is stochastic. Apart from this difference, the two words are synonyms.

One can make a randomization, but he cannot create a coincidence

My understanding is that a stochastic process is a time-based function whose value depends on its previous value and a random change. For example, if I throw a die, I will get an integer from 1 to 6 which is random. If I repeatedly throw a die and add up the cumulative sum of numbers, I have a stochastic process. 3 = 3, 3 + 4 = 7, 7 +1 = 8, 8 + 6 = 14 etc. 3, 7, 8, 14 is stochastic. The value of the stock market is stochastic.

There is no difference.

Stochastic: Greek

Aletory: Latin

Random: Old English or Old French (I think)

All these words above have the same meaning.