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 "Correlation …

Feb 21, 2023 · I would second Revuz and Yor as a readable text with most of the main classical results in the continuous case. Other options include Karatzas and Shreve and Protter's Stochastic …

Aug 1, 2020 · I am having a hard time grasping the core difference between a random variable and a stochastic process. A random variable assigns a number to every outcome of an experiment. A …

Aug 19, 2022 · Is $\| P \|_ {1,1}$ denoting $\ell_1 \to \ell_1$ operator norm? In that case it should be equal to $1$ for a stochastic matrix.

Sep 26, 2023 · This question arises from pages 14 and 15 of this review paper on quantum stochastic processes (in a section on classical stochastic processes). Suppose we have a stochastic process, …

Dec 15, 2023 · In "Reverse Time Diffusion Equation Models", Brian D.O. Anderson begins with a multidimensional Ito SDE $$ dx_t = f(x_t,t) dt + g(x_t, t) dw_t,$$ with some ...

Jul 13, 2022 · If you already have a general concept of a stochastic integral then the special version w.r.t. an Ito process follows by linearity. But the above is a definition, not a consequence. Your …

Apr 16, 2021 · I have a silly question. I know that the stochastic differential equation in derivative form is : $$d X_{t} = aX_{t}dt +b X_{t}dB_{t}$$ can be written is the integral ...

Jun 14, 2018 · where in the last step I have used the Ito isometry. Thus the process I2 − X I 2 X is a martingale and therefore a local martingale and by definition of quadratic vatiation (your definition in …