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Markov chain and joint distribution

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#stochastic-processes #markov-chains
1.9k
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Show that the hitting time of an open set for a right-continuous process is a stopping time

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#probability-theory #stochastic-processes #stopping-times #filtrations
1k
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Uniformly integrable set is bounded in $L^1$

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#stochastic-processes #stochastic-calculus #lp-spaces #stochastic-analysis #uniform-integrability
274
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Gambler's ruin with unequal bet and unequal probabilities

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#probability #stochastic-processes #markov-chains
666
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Estimate probability using forward Kolmogorov equation

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#probability #stochastic-processes #markov-chains #markov-process
144
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How to calculate this double integral? (solution known)

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#integration #definite-integrals #stochastic-processes #exponential-function #closed-form
60
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How can we prove that $\inf\left\{t\in[0,T]:X_t\ge n\right\}\wedge T\xrightarrow{n\to\infty}T$, if $\operatorname P[X_T<\infty]=1$?

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#stochastic-processes #stopping-times
424
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birth death process with single server

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#probability #stochastic-processes #markov-chains #markov-process
1.8k
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The expectation is zero

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#probability #stochastic-processes #expectation #martingales
135
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Poisson random measure with the uniqueness

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#real-analysis #probability-theory #stochastic-processes #stochastic-calculus
89
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Convergence in $L^2$ of $T_n/\mathbb{E} (T_n)\to 1$, $T_n$ be the first time a Galton Watson has more than $n$ individuals

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#probability #stochastic-processes
104
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Prove that $\inf\left\{t\ge 0:Y_t=y\right\}$ is a stopping time

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#stochastic-processes #stopping-times
77
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Showing that the Autocovariance Function of a Random Field is Positive Definite

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#probability #stochastic-processes #random-variables
109
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Extension of the stochastic integral in the book "PDE and Martingale Methods in Option Pricing"

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#probability-theory #stochastic-processes #stochastic-integrals #stochastic-analysis #stopping-times
332
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Martingale property of Brownian motion after change of measure

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#stochastic-processes #stochastic-calculus #brownian-motion #density-function

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