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In non-Ito processes, does the identity $dW^{2}=dt$ always hold?

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#integration #stochastic-processes #stochastic-calculus
482
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Stochastic integral of indicator function with respect to geometric Brownian motion

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#stochastic-calculus #brownian-motion #stochastic-integrals
184
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The probability distribution of "derivative" of a random variable

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#reference-request #stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-pde
402
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Why can you differentiate inside an infinitesimal generator?

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis #stochastic-differential-equations
230
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Prove stochastic differential relation $(dN_t)^2 = dN_t$

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#probability #probability-theory #stochastic-processes #stochastic-calculus #poisson-process
3.8k
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Proof of the union of two indicator functions

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#real-analysis #probability #stochastic-calculus
70
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"Cross Cubic variation" of Two Brownian Motions

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#probability-theory #probability-distributions #stochastic-calculus #stochastic-integrals
113
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Literature Regarding Exit Time Ito Process

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#probability #stochastic-calculus #brownian-motion #stopping-times
76
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Stochastic integral with a homogeneous Poisson process

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#stochastic-processes #stochastic-calculus #stochastic-integrals
512
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Almost sure definition of Ito's lemma but integral terms are defined in $L^2$

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#probability #probability-theory #stochastic-processes #stochastic-calculus #brownian-motion
412
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Importance of white noise and Brownian motion

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-differential-equations
432
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Solution to system of stochastic differential equations

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
357
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How can I show that $\int_0^T f(s)dW_s\sim \mathcal N\left(0, \int_0^T f(s)^2ds\right)$?

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#probability-theory #stochastic-processes #normal-distribution #stochastic-calculus #stochastic-integrals
106
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Stochastic integration with non-caglad integrand

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#probability-theory #stochastic-calculus #brownian-motion #stochastic-integrals
647
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Fourier Series of Brownian Motion $(B_t)_{t \in [0,1]}$ wrong?

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#probability-theory #stochastic-processes #fourier-analysis #stochastic-calculus #brownian-motion

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