In laymans terms: What is a stochastic process? A stochastic process is a way of representing the evolution of some situation that can be characterized mathematically (by numbers, points in a graph, etc ) over time They are of greatest help when you either don't know the exact rules of that evolution over time, or when the exact rule of that evolution is too complicated or costly to compute
Whats the difference between stochastic and random? The terms "stochastic variable" and "random variable" both occur in the literature and are synonymous The latter is seen more often Similarly "stochastic process" and "random process", but the former is seen more often Some mathematicians seem to use "random" when they mean uniformly distributed, but probabilists and statisticians don't
What is stochastic mapping? - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
terminology - What is the difference between stochastic calculus and . . . Stochastic calculus is to do with mathematics that operates on stochastic processes The best known stochastic process is the Wiener process used for modelling Brownian motion Other key components are Ito calculus Malliavin calculus Stochastic calculus is used in finance where prices can be modelled to follow SDEs
Difference between time series and stochastic process? Basically, a stochastic process is to a time series what a random variable is to a number The realization (the "result", the observed value) of a random variable (say, a dice roll) is a number - (but, as it's a random variable, we know that the number can take values from a given set according to some probability law)
Difference between statistics and stochastic? [closed] "Stochastic", on the other hand, is an adjective while both "probability" and "statistics" are nouns, denoting fields of study To say that a process is "stochastic" is to say that at least part of it happens "randomly"- so can be studied using probability and or statistics
probability theory - What is the difference between stochastic process . . . A stochastic process is a family of random variables indexed by some set, usually $\mathbb{Z}^{n}$ or $\mathbb{R}^{n}$ It's additional structure over random variables that let you establish notions of trajectories, association over a space and other interesting properties
continuity - What is a continuous stochastic process? - Mathematics . . . Isn't this violating the definition of continuous stochastic process or is it that I have to keep $\omega$ constant throught out the process ? Also, is $\omega$ in the definition of continuous stochastic process the outcome at any point of time or is it the string of the outcomes that occurs till time infinity?
random process和stochastic process的区别是什么？ - 知乎 事实证明 Khinchin 多虑了。他的苏联同行们很快就发现：什么stochastic，你这不就是random吗？整这么玄乎干什么？于是大家都直接叫random process，也没有引来什么官方的迫害。所以直到今日，很多直接从俄语翻译的文献都是用random process的。