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Independence of discrete random variable from itself (please check and comment on my attempt)?

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#probability #probability-theory #stochastic-calculus #stochastic-analysis
385
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Stochastic process as an Ito integral over time-dependent integrand (without $t$ in upper limit)

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#stochastic-processes #stochastic-calculus #stochastic-integrals
99
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Expectation of Integral

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#probability-theory #measure-theory #expected-value #stochastic-calculus #stochastic-integrals
97
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$\sum_{j=1}^n (B_{t_j}-B_{t_j^{\ast}})^2\xrightarrow{L^2}\frac{T}{2}$?

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#probability-theory #stochastic-calculus
67
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Continuous Version of Law of total probability for random variables

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#probability-theory #random-variables #stochastic-calculus
629
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Difference of two stopping times

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#probability-theory #measure-theory #stochastic-calculus #stopping-times
225
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unique solution of SDE

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#stochastic-calculus #stochastic-differential-equations
62
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Is this a stochastic integral?

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#stochastic-processes #stochastic-calculus #mathematical-modeling #stochastic-integrals
411
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Double stochastic and Riemann integral

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
974
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How do you find the variance of an Ito Integral?

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#probability #stochastic-processes #stochastic-calculus
31
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Confusion on the need to assume that $\int_{0}^{T} \lvert H_{s}\rvert \lvert d \langle X, X\rangle\rvert_{s} < \infty $ before defining integral

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#real-analysis #probability #probability-theory #stochastic-processes #stochastic-calculus
28
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$\{w \in \Omega,\theta(w) \leq u\}=\bigcup_{r \in [0,u]}\{w \in \Omega,X_r \in G\}$

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#probability-theory #stochastic-processes #stochastic-calculus
45
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Why does this expression involving covariance hold?

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#probability #stochastic-processes #stochastic-calculus #brownian-motion
74
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Showing a joint process is markov

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#stochastic-processes #stochastic-calculus #markov-process #stochastic-pde
75
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How can I get the integral process with its quadratic variation?

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#stochastic-processes #stochastic-calculus #brownian-motion #quadratic-variation

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