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RV with finite mean implies RV in $L^1$

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#probability-theory #measure-theory #lebesgue-integral #stochastic-integrals
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The closure of the elementary processes are the predictable processes

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#probability #stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
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expectation of integral of power of Brownian motion

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals
223
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Calculating Expectation of Exponential Brownian motion

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#brownian-motion #stochastic-integrals
30
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[Stochastics]: What is wrong with dX/X

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#stochastic-processes #stochastic-calculus #stochastic-integrals
55
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Itô formula's proof

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#martingales #stochastic-integrals #variance #covariance
115
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Solution of Dirichlet Problem with Itô's formula with Brownian Motion

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#brownian-motion #stochastic-integrals #expected-value
109
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Simple integrands dense in square integrable integrands

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#stochastic-integrals #expected-value #monotone-class-theorem
804
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What does it mean that $X_T$ is a solution to a Brownian Motion driven SDE ($dX_t = ....$)?

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#stochastic-processes #stochastic-calculus #stochastic-integrals
323
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Bond-price dynamics in the Vasicek model

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#stochastic-processes #stochastic-calculus #stochastic-integrals
391
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Proving Two Ito Integral Idenities

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#probability-theory #stochastic-calculus #brownian-motion #stochastic-integrals
32
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How to integrate over a random variable to get the expectancy value

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#stochastic-integrals #expected-value
69
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Is there a formula like Tanaka's for a censored process?

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#stochastic-processes #stochastic-integrals
357
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Use Ito lemma to solve some SDE

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#stochastic-calculus #stochastic-integrals
472
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Geometric Brownian motion, Itô formula

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#stochastic-calculus #brownian-motion #martingales #stochastic-integrals #stochastic-analysis

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