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Finding a regular process which is a martingale

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#stochastic-processes #martingales
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If $T_{1} \le T_{2}$ are stopping times, then $\mathcal{F}_{T_{1}} \subseteq \mathcal{F}_{T_{2}}$

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#stochastic-processes #solution-verification #stopping-times
617
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Doob's Decomposition Theorem and Uniform Integrability

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#probability-theory #stochastic-processes #martingales #stopping-times #uniform-integrability
248
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How to prove symmetric random walk is normally distributed when steps n goes to infinity

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#probability-theory #stochastic-processes #normal-distribution #random-walk #central-limit-theorem
213
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Expectation of Brownian hitting time

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#probability #stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
163
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How to prove the transition probability

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#probability #probability-theory #stochastic-processes #markov-chains #markov-process
43
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Preserving symplectic structure iff matrix has unitary determinant

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#stochastic-processes #symplectic-geometry #stochastic-differential-equations
94
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How can $\mathcal{F}_{T}$ be a $\sigma$-algebra in this context of stopping time?

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#probability-theory #measure-theory #stochastic-processes #random-variables #stopping-times
323
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Question regarding a Markov chain probability of not having visited a state

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#stochastic-processes #markov-chains #markov-process
50
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If $(X_{n})_{n \in \mathbb N}$ is a sub-martingale and $T$ a stopping time. Then $(X_{n \wedge T})_{n \in \mathbb N}$ is also a sub-martingale

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#stochastic-processes #martingales #solution-verification #stopping-times
150
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$(X_{S}, X_{T})$ is a sub-martingale with respect to the filtration $(\mathcal{F}_{S}, \mathcal{F}_{T})$

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#stochastic-processes #definition #martingales #stopping-times
688
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Can a right-continuous stochastic process be predictable?

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#stochastic-processes
232
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Markov chain example with a stopping time

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#probability #probability-theory #stochastic-processes #markov-chains #markov-process
257
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Variance of $n$-dimensional Brownian motion (Oksendal)

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#stochastic-processes #stochastic-differential-equations
147
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How to show Tanaka's formula is the Doob-Meyer decomposition?

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#stochastic-processes #martingales #stochastic-analysis

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