Question

Why $\mathbb P\left\{\sup_{s\in [0,t]}|M_s|\geq y\right\}\leq \frac{\mathbb E(|M_t|1_{\{\sup_{s\in [0,t]}|M_s|\geq y\}})}{y}$ holds?

score 69 · Answer 1 · 2021-01-24 17:58:34

Why $\mathbb P\left\{\sup_{s\in [0,t]}|M_s|\geq y\right\}\leq \frac{\mathbb E(|M_t|1_{\{\sup_{s\in [0,t]}|M_s|\geq y\}})}{y}$ holds?

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List Question

Why $\mathbb P\left\{\sup_{s\in [0,t]}|M_s|\geq y\right\}\leq \frac{\mathbb E(|M_t|1_{\{\sup_{s\in [0,t]}|M_s|\geq y\}})}{y}$ holds?

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Proving that a specific stopping time is finite a.s.

Equality of expectations in martingale

Limit of a martingale sequence

How can I prove the following conditional Expectation?

Martingale proof

How to prove that the quadratic variation of $X_t = W_t^4 - 6tW_t^2 + 3t^2$ is integrable?

How to price a contract that is denominated in another currency using the Martingale Approach to the Black and Scholes theory?

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Prove that a stochastic process is a Martingale

Stopping times and martingales expectation

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Let $\alpha > 0$, $M_t=\exp(\alpha B_t - \alpha^2 t/2)$ for all $t \ge 0$. Show that $M_t \to 0$ a.s.

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