# Questions tagged [stochastic-integrals]

This tag is used for questions about stochastic integrals – especially for calculations. For questions related to more theoretical aspects of stochastic integrals such as their constructions, (stochastic-analysis) may be more appropriate.

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### One question about exponential martingale inequality at a paper of Ann. of Math.

I saw a strange inequality about martingales: If $\operatorname{M}\left(s,t\right)$ is an continuous $L^{2}$ martingale start at $s$, $\left[\operatorname{M}\right]\left(s,t\right)$ is its quadratic ...
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### Stochastic Integral and Ito's Isometry: Sharp-bracket process [M] or Angle-bracket process <M>?

I am learning stochastic integral, and I have noticed that the Ito's Isometry is sometimes stated using the quadratic variation process $[M]$ (e.g., pg. 47, Eq. (27.3), vol. 2 of Rogers & William),...
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### Proving that the expected value of an $L^2$ approximation of $\int_{0}^{T} B_t^2 \,dt$ by simple functions goes to 0 as $n \to \infty$
Let $B = (B_{t})_{t \geq 0}$ be a 1-dimensional Brownian motion on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$ (i.e. that is, $B_t: \Omega \to \mathbb{R}$ for each $t \geq 0$), and let \$T &...