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Martingale property and conditional expectation

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #stochastic-analysis
65
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Martingale and $L^4$-integrability

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#probability-theory #stochastic-processes #martingales
59
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Determine $\mu \in \mathbb{R}$ so that an adapted process is a martingale and give the Doob decomposition of that adapted process

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#probability-theory #stochastic-processes #martingales
155
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Questions of the Proof of Kolmogorov's Strong Law of Large Numbers

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#probability-theory #martingales #law-of-large-numbers
331
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Doob's Martingale Decomposition -- Proving that the Martingale component is indeed a Martingale

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#probability-theory #stochastic-processes #conditional-expectation #martingales
41
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Show that $W(Y_{\tau \land k})$ is a martingale where Y is a Markov chain and that it converges almost surley

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#stochastic-processes #markov-chains #martingales #markov-process #random-walk
48
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Choosing the stake before flipping a coin

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#stochastic-processes #conditional-expectation #martingales
186
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Optimal strategy for doubling money in an unfair game

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#conditional-expectation #martingales
44
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Convergence of likelihood function

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#probability #martingales
184
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A stopping time problem for a random walk with transition probabilities dependent on states

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#probability #martingales #markov-process #random-walk #stopping-times
136
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Conditional Expectation of Integral over square of Brownian Motion - PDE Approach

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#stochastic-processes #stochastic-calculus #martingales #heat-equation
91
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Martingale processes

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #stochastic-pde
745
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Gambler's Ruin: Expected time of ruin using martingale and stopping time

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#stochastic-processes #martingales #stopping-times
110
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Optional sampling theorem with $L^2$ bounded martingale with stopping time

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#probability-theory #stochastic-processes #martingales #stopping-times
154
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A gambler's fortune converges 0 or 1? (Martingale convergence theorem)

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#probability #stochastic-processes #martingales #gambling

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