List questions from quadratic-variation

Published on 22 Jan 2014 - 18:16

399

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Cross variation not independent Brownian motions

Published on 26 Feb 2014 - 17:38

762

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Quadratic variation - Semimartingale

Published on 04 Mar 2014 - 3:17

655

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Show that $M-M_0$ is an $L^2$ bounded martingale if $E([M]_\infty)<\infty$.

Published on 23 Feb 2026 - 13:27

344

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Azema martingale and quadratic covariation

Published on 13 Apr 2017 - 20:31

133

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Prove that $Z_n=\sum_{i=0}^{n-1}Y_{t_i}(M_{t_{i+1}}-M_{t_i})(N_{t_{i+1}}-N_{t_i})$ converges to $\int_{0}^t Y_s\,d[M,N]_s$ in probability

Published on 14 Apr 2017 - 4:10

256

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Brownian motion properties

Published on 22 Apr 2017 - 19:40

491

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Show that the quadratic variation $\left[W\right]$ of a $Q$-Wiener process $W$ is given by $\left[W\right]_t=tQ$ for all $t\ge0$

Published on 30 Apr 2017 - 19:16

130

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Show that the quadratic variation has a nondecreasing modification

Published on 21 May 2017 - 13:48

189

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Show that $\sup\limits_t\left|X_t^n\right|\to0$ in probability iff $\lim\limits_{t\to\infty}[X^n]_t\to0$ in probability when $n\to\infty$

Published on 21 May 2017 - 20:56

1.4k

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If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

Published on 22 May 2017 - 20:44

269

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Definition quadratic variation

Published on 30 May 2017 - 11:23

378

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Semimartingale property of function of Brownian motion

Published on 23 Feb 2026 - 15:09

512

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Is a local continuous martingale square integrable.

Published on 23 Feb 2026 - 15:03

258

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Show that semimartingale related to Brownian motion is local martingale

Published on 23 Feb 2026 - 15:09

List Question

Bilinearity of quadratic variation

Cross variation not independent Brownian motions

Quadratic variation - Semimartingale

Show that $M-M_0$ is an $L^2$ bounded martingale if $E([M]_\infty)<\infty$.

Azema martingale and quadratic covariation

Prove that $Z_n=\sum_{i=0}^{n-1}Y_{t_i}(M_{t_{i+1}}-M_{t_i})(N_{t_{i+1}}-N_{t_i})$ converges to $\int_{0}^t Y_s\,d[M,N]_s$ in probability

Brownian motion properties

Show that the quadratic variation $\left[W\right]$ of a $Q$-Wiener process $W$ is given by $\left[W\right]_t=tQ$ for all $t\ge0$

Show that the quadratic variation has a nondecreasing modification

Show that $\sup\limits_t\left|X_t^n\right|\to0$ in probability iff $\lim\limits_{t\to\infty}[X^n]_t\to0$ in probability when $n\to\infty$

If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

Definition quadratic variation

Semimartingale property of function of Brownian motion

Is a local continuous martingale square integrable.

Show that semimartingale related to Brownian motion is local martingale

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