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Why is $E[\ \sup_{ 0\leq u \leq t } |X_u|\ ]<\infty$ where $X$ is a right continuous submartingale?

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#stochastic-processes #stochastic-calculus #martingales #stochastic-analysis
2.3k
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Stochastic Leibniz Rule

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#proof-verification #self-learning #stochastic-calculus #stochastic-integrals #stochastic-analysis
453
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Kullback–Leibler divergence as Exponential cone

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#optimization #convex-optimization #stochastic-analysis
316
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Martingale property of a stochastic integral w.r.t. a local martingale.

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#martingales #stochastic-integrals #stochastic-analysis #local-martingales
806
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Stochastic Taylor Expansion of Ito Integral

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#stochastic-processes #taylor-expansion #stochastic-calculus #brownian-motion #stochastic-analysis
59
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Where exactly in the proof is the boundedness of $\sigma(x)$ and $b(x)$ being used?

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#stochastic-processes #stochastic-integrals #stochastic-analysis
501
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Solving a PDE (HJB equation for a simple stochastic control problem)

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#partial-differential-equations #stochastic-analysis #optimal-control
129
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Expectation of a stopping time containing BM

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#probability #expectation #stochastic-analysis #stopping-times
45
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How can I show that $\mathcal{F}_t^X$ is generated by sets of the form $F=\{(X_{t_1},\dots, X_{t_n}) \in \Gamma\}$

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#stochastic-processes #stochastic-calculus #stochastic-analysis #filtrations
130
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What is the solution to SDEs of the form $dx=f(x)(dt+\rho dW_t)$?

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#stochastic-processes #stochastic-calculus #stochastic-analysis #stochastic-differential-equations
960
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Prove that $\tau$ is a stopping time

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#stochastic-processes #stochastic-analysis #stopping-times
184
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Stochastic process’ mean-square derivative $X'(t)\equiv 0$ implies $X(t) \equiv X$?

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#stochastic-processes #stochastic-calculus #stochastic-analysis
55
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What are the generating sets of $\mathcal{F}_t^X=\sigma(X_s , 0 \leq s \leq t) $?

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#stochastic-processes #stochastic-calculus #markov-process #stochastic-analysis #filtrations
24
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How to define the following stochastic integrals?

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#stochastic-processes #stochastic-calculus #stochastic-analysis
328
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Where is the Strong Markov property(SM) being used in the proof that augmented filtration of a Strong Markov process is right continuous?

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#stochastic-processes #stochastic-calculus #markov-process #stochastic-analysis #filtrations

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