Oct 8, 2015 · A stochastic process is a colection of random variables defined on the same probability space. Please explain further what parts of this definition are escaping you.

Feb 28, 2012 · What's the difference between stochastic and random?There is an anecdote about the notion of stochastic processes. They say that when Khinchin wrote his seminal paper …

Feb 19, 2024 · The answer here makes sense to me, in the sense that the stochastic integral does not preserve the local martingale property if the integrand is not predictable, but I am …

Oct 29, 2021 · I would like to define stochastic integral of caglad process with respect to semimartingale. Can I define this integral as the sum of Lebesgue-Stieltjes integral and …

Apr 19, 2023 · How to properly define a stochastic process as a random variable valued in the Skorokhod space Ask Question Asked 2 years, 4 months ago Modified 2 years, 4 months ago

Dec 1, 2015 · "Itô integration" and "stochastic integration" Actually Itô integration is a particular form of stochastic integration. There are also other ways to define stochastic integrals. …

Jan 12, 2023 · My question is about the definition of a stochastic process. From the definition of the majority of textbooks, we know a stochastic process is defined as a collection of random …

Aug 4, 2016 · For example, any set of time series data such as a set of stock price data at hand is a "function of time", which is mathematically viewed as a realization of a stochastic process. …

For a stochastic process, Can it be allowed that the state space and the $\sigma$-algebra on it is different for different value of the index? Is it correct that, as a stochastic process, "a random …

Aug 4, 2022 · 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 …