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Understanding a proof of Doob's optional sampling theorem

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#probability #stochastic-processes #martingales
40
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$\int_0^t(g(s)X_1(s)+f(s)X_2(s))dWs$ - local martingale

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#stochastic-processes #stochastic-calculus #stochastic-integrals #local-martingales
138
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Every submartingale has a left-continuous modification

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#stochastic-processes #martingales
85
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Explanation of Proof of Theorem 43 of Chapter 4 of Protter's Stochastic Integration

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#probability-theory #stochastic-processes #proof-explanation #martingales
60
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Properties of Expectations and Correlations on Probability

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#probability-theory #stochastic-processes
115
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Expected value of product of two Ito Integrals

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#stochastic-processes #stochastic-calculus #expected-value #stochastic-integrals
89
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Understanding stochastic Big-$O$ notation in a stochastic process context

Published on
#statistics #stochastic-processes #asymptotics #probability-limit-theorems
237
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stochastic integral is unique

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#analysis #stochastic-processes #stochastic-calculus
66
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Prove that the value function $u$ satisfies this system of linear equations

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#stochastic-processes #markov-chains #solution-verification #stopping-times
96
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Prove that process satisfy Bessel equation

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
113
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PDF and CDF of Ratio distribution in specific cases

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#probability #probability-theory #probability-distributions #stochastic-processes
102
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Is it possible to prove that (almost surely) a path of a scaled random walk does not converge to any function on $C[0,1]$?

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#stochastic-processes #brownian-motion #random-walk
134
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Uniform integrability of positive part of submartingale

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#probability-theory #stochastic-processes #martingales
54
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Explicit solution of SDE

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis
133
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Properties of a Brownian motion

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#stochastic-processes #brownian-motion #expected-value

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