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Show that $Y_t = (W_t + t)\exp\{-W_t - \frac{1}{2}t\}$ is a martingale.

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#probability-theory #stochastic-calculus #martingales
342
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Proving integrability of the martingale $\cosh(\lambda B_t)\textrm{e}^{-\frac12\lambda^2t}$

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#integration #expected-value #brownian-motion #martingales
593
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Proving that a infinite sum of random variables converges

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#probability #probability-theory #martingales #bmo-martingales
25
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sequence of bounded random variables form martingale then they are uncorrelated

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#martingales #covariance
35
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Diameter of finite and bounded martingales

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#probability-theory #reference-request #martingales
81
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$E(M_{n\wedge \tau}) = E(M_0)$ implies $M$ is a martingale

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#probability #probability-theory #martingales
103
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$(f(X_n))_{n \in \mathbb{N}_0}$ martingale implies $f'' = 0$?

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#stochastic-processes #stochastic-calculus #martingales
218
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Laplace transform of time until absorption of Brownian motion

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#stochastic-processes #stochastic-calculus #martingales #stochastic-analysis #stopping-times
55
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Super-tough expectation computation

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
42
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Poisson Process and proving conditional probability

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#probability #probability-theory #conditional-expectation #martingales #poisson-process
166
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Quadratic variation of a process

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#stochastic-processes #random-variables #brownian-motion #martingales #quadratic-variation
259
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Proof that squared Poisson process is martingale

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#measure-theory #stochastic-processes #martingales
66
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Ito processes and Martingales

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#stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
222
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Show integrability of convex (and increasing) function of martingale (submartingale)

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#integration #probability-theory #measure-theory #stochastic-processes #martingales
129
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Conditions for quadratic variation

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#integration #random-variables #brownian-motion #martingales #quadratic-variation

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