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identifying a time period spent in a place that is longer than expected by chance

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47
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Passage time of a Brownian motion

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#reference-request #stochastic-processes #brownian-motion #stopping-times
116
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Future of martingale after stopping time

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#probability-theory #stochastic-processes #conditional-expectation #martingales #stopping-times
255
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Finding the expected stopping time of random walk

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#probability #expected-value #random-walk #stopping-times
153
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Bound on expectation of minimum of two stopping times (proving integrability)

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#probability-theory #stochastic-processes #conditional-expectation #martingales #stopping-times
204
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Exercise 3.13 Paolo Baldi stochastic calculus: bounds on Brownian motion

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72
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Attempt to improve from $L^1$-boundedness to uniform integrability

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#probability-theory #stochastic-processes #random-variables #martingales #stopping-times
64
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Brownian motion with a stopping time

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#real-analysis #probability-theory #stochastic-processes #brownian-motion #stopping-times
52
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The maximum of $W_t-t$ with respect to $t$

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#probability-theory #brownian-motion #stopping-times
46
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Stopped version of UI martingale is UI

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#probability-theory #measure-theory #martingales #stopping-times #uniform-integrability
174
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Showing integrability of random variable at stopping time

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#probability-theory #stopping-times
168
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Write probability of first return time in terms of first hitting time

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#probability #probability-theory #stochastic-processes #markov-chains #stopping-times
238
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Show that $\tau = \inf \{n \in \mathbb{N}: X_n \in \{a, -b\}\}$ is a stopping time

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#probability-theory #stochastic-processes #stopping-times
126
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Doob decomposition / stopping time

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45
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If $\tau$ is an $\mathcal F$-stopping time, is $\{\tau<t\}\in\mathcal F_t$? (Even for $t=\infty$)?

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