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Solution to Dirichlet is necessarily given by Brownian Motion (problem with stopping times)

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#probability-theory #partial-differential-equations #stochastic-processes #stochastic-calculus #brownian-motion
1.1k
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Calculating the expectation of the supremum of absolute value of a Brownian motion

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#brownian-motion #absolute-value #supremum-and-infimum #expected-value
27
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brownian translation

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#probability-theory #stochastic-processes #random-variables #brownian-motion
299
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Conditional expectation of Brownian motion's first hitting time

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#probability-theory #stochastic-processes #brownian-motion #conditional-expectation #stopping-times
259
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Show a stochastic process is a Martingale

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#stochastic-calculus #brownian-motion
34
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Distribution of $(X,Y,Z)$, $X=W(3)-W(1), Y=W(5)-W(2), Z=W(7)-W(4)$. (Brownian motion)

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#measure-theory #stochastic-processes #brownian-motion
617
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Markov property for 2 dimensions and example

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#stochastic-processes #brownian-motion #markov-process
350
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$\mathbb E[W_s^2W_t^2]$ for Brownian motion

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#stochastic-processes #brownian-motion
123
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Question on Construction of Brownian motion with Kolmogorov-Centsov Theorem

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#probability-theory #measure-theory #continuity #brownian-motion #borel-sets
564
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W_t^3 martingale or not? two arguments puzzle me.

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#probability #brownian-motion #martingales
256
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Showing Ito's formula gives a semimartingale decomposition for brownian motion

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#stochastic-calculus #brownian-motion #stochastic-integrals
121
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Understanding where the Mandelbrot Van Ness representation of fractional brownian motion comes from

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#reference-request #brownian-motion
461
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Probability of $B_t < 0$ if $B$ is Brownian Motion

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#stochastic-processes #brownian-motion
3.4k
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First variation on Brownian motion

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#stochastic-calculus #brownian-motion
2k
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Product of two independent brownian motion is a martingale

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#probability-theory #brownian-motion #martingales

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