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Find $S_Y(f)$ with given $H(f)$ and $S_X(f)$

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#stochastic-processes
30
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Inverse of Poisson process.

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#probability #stochastic-processes #poisson-process
196
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Distribution of Brownian Motion with drift

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
154
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Show this statement holds for a right continuous martingale.

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#probability-theory #stochastic-processes #martingales
71
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$\mathbb{E}(\int_{\rho}^{\tau}X(s)dW(s)\cdot\int_{\rho}^{\tau}Y(s)dW(s)|F_{\rho})=\mathbb{E}(\int_{\rho}^{\tau}X(s)Y(s)ds|F_{\rho})$

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#probability #stochastic-processes #stochastic-calculus #stochastic-integrals
806
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$Var (X_n)= Var(X_0) +\sum_{k=0}^{n} Var (X_{k}-X_{k-1})$, Martingale Variance

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#probability-theory #stochastic-processes #conditional-expectation #martingales
23
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Simplify the following transfer function

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#stochastic-processes
193
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How to infer the average speed of a frog?

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#reference-request #stochastic-processes #random-variables #statistical-inference #stationary-processes
168
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Solve a system of SDEs

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#stochastic-processes #stochastic-differential-equations
82
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$\sigma$-algebra of the past intersection property

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#probability-theory #measure-theory #stochastic-processes #martingales
53
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Find supremum of $( X_t -x)^2$

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
636
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Expected value for a system of SDE's

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#stochastic-processes #stochastic-calculus #expected-value #stochastic-differential-equations
49
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Could indicator function be introduced into probability?

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#probability #stochastic-processes #markov-chains #conditional-probability
52
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$X=M+A$ bounded semimartingale, then $M$ and $A$ are bounded? Counterexample?

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #local-martingales
43
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A type of convergence of random variable

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#probability-theory #measure-theory #stochastic-processes #random-variables

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