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Clark-Ocone Formula for computing SDE

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#probability-theory #stochastic-processes #stochastic-integrals #stochastic-analysis #malliavin-calculus
126
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Extend the definition of martingale to nonnegative random variables.

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#probability-theory #measure-theory #stochastic-processes #martingales
37
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If each $(B^n)_{t\in[0,\:T]}$ is $\mathcal F$-adapted, then $\sigma\left(\bigcup_{n\in\mathbb N}\sigma\left(B^n_s:s\le t\right)\right)=\mathcal F_t$

Published on
#measure-theory #stochastic-processes #filtrations
99
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A question about random walk in Markov chain

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#stochastic-processes #markov-chains #random-walk
361
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Given a fixed filtered probability space, can we prove the existence of a Brownian motion on it?

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#stochastic-processes #brownian-motion
342
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Martingale and composition of function

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#probability-theory #stochastic-processes #martingales
735
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Expected Value and Variance of a process (Itô's lemma, brownian motion)

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#probability #stochastic-processes #brownian-motion #variance
26
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Show the necessary conditions for the following stationary process to be real-valued

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#probability #stochastic-processes
55
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How to get a martingale?

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#probability #probability-theory #stochastic-processes #martingales
759
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Misunderstanding of dirac measure in conjunction with point process

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#probability-theory #measure-theory #stochastic-processes
223
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Hint :Expected value of a stochastic process

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#ordinary-differential-equations #stochastic-processes #stochastic-calculus
933
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Conditioning on Brownian motion when $t\in[0,s)$

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#stochastic-processes #brownian-motion #conditional-expectation
126
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Are these two scenarios equivalent ? (random walks on chessboard)

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#probability #stochastic-processes #random-walk
385
Views

Intuition of (local) ergodicity and ergodicity breaking

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#stochastic-processes #ergodic-theory #mixing
377
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Find the transition function of the process

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#stochastic-processes #markov-process

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