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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
- Books recommendations on stochastic analysis - Mathematics Stack Exchange
Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models These two books are very good if you want to apply the theory to price derivatives Stochastic Differential Equations: An Introduction with Applications Bernt Oksanda
- How does one interpret the meaning of a stochastic derivative?
Only the integral with respect to Brownian motion is defined in the Ito- or the Stratonovich calculus This means that there is no "stochastic derivative", and that the notion of "velocity" is undefined for Brownian motion There just is no room for the interpretation of a "velocity" in physical terms in the theory
- 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
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