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$(X_n ; n>0)$ gaussian random variable sequence, converges uniformly, implies that $X_n$ converges in $L^2$

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#probability #stochastic-processes #random-variables
556
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Proving that a random walk that diverges to infinity may not become negative

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#probability-theory #stochastic-processes #random-walk #stopping-times
2.4k
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Prove stochastic exponential to be a martingale

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#probability #stochastic-processes #martingales #stochastic-integrals #stochastic-pde
52
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Martingale ganerated by random walk

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#probability-theory #stochastic-processes #markov-chains #martingales #random-walk
816
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How to verify if process is Markov stochastic process with discrete time?

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#probability-theory #stochastic-processes #markov-chains #markov-process
201
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Apply Ito Lemma and find process

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#stochastic-processes #stochastic-calculus
46
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Pathwise closeness of solutions of SDE's

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
434
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existence of two intercommunicating states that have the same period in a homogeneous markov chain

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#probability #probability-theory #stochastic-processes #markov-chains #markov-process
115
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Does $Z(t)$ have stationary increments?

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#probability #stochastic-processes #brownian-motion #stochastic-integrals
640
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Laplace Transform of Stopping Time of Brownian Motion

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#measure-theory #stochastic-processes #stochastic-calculus #brownian-motion #stopping-times
2.8k
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Doob's decomposition of a submartingale

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#probability-theory #stochastic-processes #conditional-expectation #martingales
358
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How to construct a Poisson process not based on Lebesgue measure?

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#probability #probability-theory #stochastic-processes
828
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Probability approach in the expected payoff of a dice game

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#probability #statistics #stochastic-processes
537
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What's the expected stopping time for a sum of random variables to cross a threshold?

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#stochastic-processes #stopping-times
158
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If $f$ is a measurable random field, then $(ω,x)↦E[f(x)\mid F](ω)$ has a measurable version $g$ and $E[f(X)\mid F]=g(X)$ for all $F$-measurable $X$

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#probability-theory #stochastic-processes #conditional-expectation #stochastic-analysis

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