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Localization lemma in Ito Integral

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#stochastic-calculus #stochastic-integrals #stochastic-analysis
32
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Showing $V_t$ is independent of $B_t^{(1)}$ in this SDE

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#stochastic-calculus #expected-value #stochastic-integrals #stochastic-differential-equations
101
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Hitting time stochastic process

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#stochastic-processes #stochastic-calculus
95
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continuous differentiable function applied to a Brownian motion not square integrable

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-analysis
741
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Solving an SDE with Ito's Lemma

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
186
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Multidimensional Fokker-Planck equation with exact solution

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
2.5k
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Showing that Ito's integral of deterministic function follows a normal distribution

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-differential-equations
175
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Equivalence of "differential" and "integral" forms in Itô calculus

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#stochastic-calculus #differential-forms #stochastic-differential-equations
70
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Given the law of a diffusion $dX_t = \lambda_t(t,X_t) + \sigma dB_t$, can we find explicitly the drift?

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis #stochastic-differential-equations
161
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Almost Sure Convergence in Martingales

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#probability-theory #stochastic-calculus #martingales
531
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Determining if an SDE defines a Gaussian Process

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#stochastic-processes #stochastic-calculus #brownian-motion
117
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Find the quadratic covariation between $[B^2,B^3]_t$

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#stochastic-calculus #brownian-motion #stochastic-integrals
249
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Mean of exponential Ito integral

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#calculus #probability #integration #stochastic-processes #stochastic-calculus
142
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Probability of Wiener process infimum

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#stochastic-processes #stochastic-calculus #stochastic-analysis
85
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$\lambda P( \min_{1 \leq k \leq n}X_k\leq -\lambda) \leq \int_{\{\min_{1 \leq k \leq n}X_k> -\lambda\}}X_ndP - E[X_0]$

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#probability-theory #measure-theory #stochastic-processes #stochastic-calculus #martingales

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