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Proving completeness of $\mathcal H^p$

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#functional-analysis #measure-theory #stochastic-analysis
65
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$\mathbb E[|X_T|]$ when $\mathbb E[T]<\infty$

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#stochastic-processes #expected-value #stochastic-analysis #stopping-times
274
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Visualize Itô differentiation rule

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#derivatives #stochastic-calculus #alternative-proof #stochastic-analysis #visualization
407
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Covariation of product of local martingales

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#stochastic-processes #martingales #stochastic-analysis #quadratic-variation #local-martingales
213
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Can finite variation martingales be approximated by martingales of integrable variation?

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#functional-analysis #measure-theory #stochastic-processes #martingales #stochastic-analysis
338
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Right-continuous and Progressively measurability of Lebesgue-Stieltjes integrals

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
55
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Decreasing variance of conditional expectation?

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
132
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Martingale is preserved under enlargement to a filtration with usual conditions

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#stochastic-processes #stochastic-calculus #martingales #stochastic-analysis
283
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Quadratic variation of a Lévy process is finite and itself a Lévy process

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#stochastic-processes #stochastic-integrals #stochastic-analysis #levy-processes
62
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Natural filtration of a Markov process

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#stochastic-processes #markov-process #stochastic-analysis
1.4k
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Brownian Motion with Optional Stopping Theorem (OST)

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#brownian-motion #stochastic-analysis
211
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Tail of hitting times for Brownian motion on the circle

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#probability-theory #brownian-motion #stochastic-analysis
596
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Skorohod convergence (space of right continuous functions with left limit)

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#functional-analysis #probability-theory #stochastic-processes #stochastic-analysis #skorohod-space
580
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About the increasing process in the Doob-Meyer decomposition

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#probability #stochastic-processes #stochastic-analysis
71
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If $dX_t=b_tdt+\sigma_tdW_t=\tilde{b}_tdt+\tilde{\sigma}_tdW_t$ then $b_t=\tilde{b}_t$ and $\sigma_t=\tilde{\sigma}_t$ a.s

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#probability-theory #stochastic-processes #stochastic-analysis

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