# Tag Info

Accepted

### Angle bracket and sharp bracket for discontinuous processes

Let $(X_t,\mathcal{F}_t)_{t \geq 0}$ be an (càdlàg) $L^2$-martingale, i.e. a martingale which satisfies $$\sup_{t < \infty} \mathbb{E}(X_t^2)<\infty.$$ Then it follows from the Doob-Meyer ...
• 113k
Accepted

• 113k
Accepted

• 85k

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### Quadratic variation of Brownian motion and almost-sure convergence

If the diameter of the $n$-th partition converges (to zero) fast enough, namely if it is of order less than $1/\log(n)$, then the quadratic variation converges almost surely. If not, then not in ...
• 81
Accepted

• 272k
Accepted

### Stochastic Exponential - Protter

Any càdlàg function $f: [0,T] \to \mathbb{R}$ has at most finitely many jumps with jump size $>\epsilon$ for any (fixed) $\epsilon>0$, see e.g. this answer. The estimate "$\leq [X,X]_t$&...
• 113k
Accepted

### Trying to compute the quadratic covariation

There is the following general statement which is helpful for the second approach Let $\psi$ be a progressively measurable function such that $\mathbb{E}\int_0^T \psi(t)^2 \, dt < \infty$ for ...
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• 113k