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List Question

first-hitting-time and conditional probability

How can we apply the optional sampling theorem for the martingale $\operatorname P\left[A\mid\mathcal F_t\right]$?

Hitting times by Brownian motion

Conditional expectation of Brownian motion's first hitting time

Hitting time into closed sets for strong markov Processes $(X_t)_{t\geq 0}$ (Peskir & Shiryaev)

Very simple gambler's ruin, Martingale and optional stopping theorem

Expectation of the exponent of a constant times exiting time of a Brownian motion (i.e. $\mathbb{E}_x[e^{n\sigma}]$)

If $T_{U,V}=\inf\{t:B_t \notin (U,V)\}$ does $\int E[B_{T_{U,V}}|U,V]dP=\int E[B_{T_{u,v}}]dP_{U,V}$

Second moment of Continuous Time Markov Chain hitting time

Show convergence of the Lebesgue integral of some expectations

Equivalent in fair price

$P(T_0 <\infty) = 1 - \lim_{k \to \infty} P(T_0 = k)$?

Martingale conditioned on sigma algebra of stopping time

Probabilistic solution to the Dirichlet problem with Dynkin formula

Wald's equation for a sum of functions of random variables

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