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- 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
- 「Stochastic」与「Random」有何区别？ - 知乎
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- What are the prerequisites for stochastic calculus?
-Theories of convergence of stochastic processes-Theory of continuous-time stochastic processes, Brownian motion in particular This is all covered in volume one of Rogers and Williams' "Diffusions, Markov processes and martingales", and also sporadically in the two probability-related books above by Dudley and Ash and Doleans-Dade
- 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)
- 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
- 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?
- 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
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