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Conditional expectation wrt an increasing family of $\sigma$-algebras

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Is an almost surely decreasing stochastic process a supermartingale?

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231
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How does Kakutani's theorem imply consistency of the likelihood ratio estimator?

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#probability #probability-theory #statistics #stochastic-processes #martingales
171
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continuous martingale are always bounded?

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#stochastic-processes #martingales #stochastic-analysis #upper-lower-bounds
65
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bounds of stopped martingale

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#stochastic-processes #martingales #stopping-times
71
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Martingale at increasing stopping times is a martingale

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#probability #probability-theory #stochastic-processes #martingales
146
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2 questions on cross-variation

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148
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Convergence of a sequence of martingale

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#probability #probability-theory #stochastic-processes #martingales #probability-limit-theorems
188
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Cross Variation of Ito Integral with $L^2$ bounded continuous martingale

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #quadratic-variation
29
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Detail in proof of $\sup\limits_tM_n(t)\overset{P}{\to}0\iff[M_n]_{\infty}\overset{P}\to 0.$

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#probability-theory #proof-explanation #martingales
41
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Complex Expansion of Exponential

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#complex-analysis #probability-theory #martingales
56
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Is the following process a martingale?

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#stochastic-processes #stochastic-calculus #brownian-motion #martingales #stochastic-analysis
41
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Question on martingales and expectations

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#probability-theory #expected-value #martingales
73
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Martingale example

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#martingales
68
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Martingale means $E[W(X_t-X_s)]=0$ for W independent on $f_s$?

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