Stochastic Processes: Movements
In probability, there is often debate between lack of knowledge versus randomness. People assign different probabilities to the same events because of the subjective nature of probability. A stochastic process is a collection of random variables reflecting for example the outcomes of repeated coin flips. A stochastic process can be discrete or continuous. A stochastic process can have drift. Really what a stochastic process tells us though is something may arise from utter randomness and that is okay. We can still proceed with modeling that phenomenon because we can define the phenomenon in terms of randomness with a positive drift for example. Life for example is largely random but the meaningful part is the drift which can be isolated. The stock market is also largely random but the upward drift is remarkable. A stochastic process definition in other words allows us to perceive what randomness really is: it is winnings that do not result from skill, and losing that do not result from mistakes, in short, randomness is not meaninglessness but meaning that does not come from anywhere that makes the model useful. Usefulness is the ultimate judge of whether a model is appropriate. If you find yourself spewing out randomness for example in conversation, you probably know you are imposing meaning which does not come from anywhere useful. Notably, there still is meaning, as useless meaning can be just said to be an insecurity. Suppose you go over to another world, incarnate into another world, to be with someone you love, and you get caught by authorities in that world and put to an end. You are still alive in your own world but in a sense you’ve lost that person you wanted to be with. She only exists in one place and that is in that world. All else is a dream for her. But I think the lesson really is that randomness is the bridge between worlds, as what I say in my world has meaning in my world but also randomly has meaning in another person’s world. And the drift which is the all-important criteria in the long-run: the drift on my randomness which may be minor in my world may be strong in her world, as my life in her world is another stochastic process. In short I’m not even arguing for cointegration or a relationship between my life and my life in her world, only in fact that my life in her world was independent, and the meaning of what happened in her world is nonexistent: all the meaning lies in mine where I’ve grown up. Perhaps the resemblance to the parable in the New Testament should stand as I discuss religion with probability to introduce rationality in both subjects whether or not you believe, and just like Voltaire wrote: the meaning was not for the rats in the ship, the meaning of the parable of the New Testament is really about something outside this world such that it started as a random process but became a random process with drift: a life became a life well-lived, and what was left for his followers in the world he left behind was simply a promise that he would return. In my case I think if I were ever in such a position I would never return since there was too much randomness in the first life that a second life would take meaning from the first for randomness is just the promise of meaning down the line.