1
vote
2answers
52 views

Inequality- Absolute Value general powers

Iam trying to understand the following inequality:$p>0$ Let $$T_{m}:=\sum_{i=1}^{m}\left(\left|\int_{\frac{i}{n}}^{\frac{i-1}{n}}g(s)dW_{s}\right|^{p}-\left|g ...
2
votes
0answers
108 views

Quadratic variation process of $G$–Brownian motion

I would like to prove the inequality $$\hat{\mathbb{E}}\left[\left(\int^T_0 \eta_t d \langle B \rangle_t \right)^2\right] \leq C \hat{\mathbb{E}}\left[ \int^T_0 \eta^2_t dt \right],$$ where $\langle B ...
0
votes
1answer
36 views

Is it true that $X(t)^a > K \iff X(t) > K^\frac1a$

Let $a \in \mathbb{N}$, $K \in \mathbb{R^+}$ and $X(t)$ be a geometric Brownian Motion. Is the following true? $$X(t)^a > K \iff X(t) > K^\frac1a$$ The context of the above is that I want to ...