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Possible example of stopped martingale not being in $L^1$

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#probability-theory #stochastic-processes #martingales #stopping-times
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How to prove this process to be a martingale?

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#probability #probability-theory #stochastic-processes #conditional-expectation #martingales
32
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How to prove that $E(M_n 1_{F})=E(M_r 1_{F})$ for a discrete-time martingale $M_n$ with $r>n$?

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#probability-theory #stochastic-processes #martingales
759
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Expected value of a standard Brownian motion

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#probability #normal-distribution #expected-value #brownian-motion #martingales
57
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Show $\mathbb{E}_1\big[S_n\textbf{1}_{\{T_{\text{hit zero}} > n\}}\big] \not\to 0$ for SSRW.

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#probability-theory #martingales #stopping-times
34
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Conditional expectation of this stochastic process?

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#stochastic-processes #conditional-expectation #martingales
83
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One of inequalities in the proof of Martingale transforms convergence

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#probability #probability-theory #martingales
101
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Showing that a random process is a martingale

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#probability-theory #stochastic-processes #martingales
139
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Convergence in distribution for sum of products of random variables

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#probability-theory #martingales #probability-limit-theorems
118
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Martingale and finite stopping time

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#martingales #stopping-times
287
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Weak solution of SDE, Tanaka equation

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #stochastic-differential-equations
66
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Limit using Itô isometry

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion #martingales
141
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Zero-mean random variable for the number of descents

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#probability #conditional-probability #martingales
55
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Condition for martingale

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion #martingales
32
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Conditional expectation equation containing martingales

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#probability-theory #conditional-expectation #martingales

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