List questions from stochastic-processes

Published on 13 Apr 2026 - 20:40

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sigma algebra representing information

Published on 16 Apr 2026 - 14:10

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Law of a stochastic processes with continuous path

Published on 20 Apr 2026 - 12:01

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Let $\xi_{n}=X_{n}-X_{n-1}$ where $EX_{0}^{2}, \sum\limits_{m}E\xi_{m}^{2} < \infty$ then $X_{n} \to X_{\infty}-$a.s. and $L^{2}$

Published on 17 Apr 2026 - 21:59

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Expected value of function of Markov chain

Published on 02 Apr 2026 - 5:05

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Stopping time and its probability showing $\mathbb{P}(\exists n \in \mathbb{N}_{0} : \sum_{k=1}^{n}V_{k} > a) \leq e^{-\lambda a}$

Published on 26 Mar 2026 - 16:26

1.3k

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$P_{ij}=0$ if state $i$ is recurrent and it does not communicate with $j$

Published on 13 Apr 2026 - 7:51

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Show $\lim\limits_{\delta \to 0} E(\vert F((X_{t_{i}}+t_{i}B_{1})_{1 \leq i \leq n})-F(X)\vert A_{\delta}]=0$

Published on 15 Apr 2026 - 10:49

202

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Is expectation of an Ito integral always 0, regardless of the limits?

Published on 12 Apr 2026 - 6:57

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Time homogeneity and Markov property

Published on 17 Apr 2026 - 10:38

65

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$E(X_1X_2X_3X_4)\leq E(X_i^4)$ for some $i\in\{1,2,3,4\}$?

Published on 16 Apr 2026 - 6:44

64

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Find expectation $ E[S]$

Published on 16 Apr 2026 - 2:33

33

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Showing that $M_{\tau}$ and $M_{\tau \land n}$ are integrable

Published on 16 Apr 2026 - 4:18

301

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Prove that the Markov chain is irreducible and recurrent

Published on 15 Apr 2026 - 17:16

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If a process is 0 up to a stopping time, then the ito integral up to the stopping time is 0.

Published on 17 Apr 2026 - 15:35

List Question

How to derive this step in a book called Brownian motion calculus?

sigma algebra representing information

Law of a stochastic processes with continuous path

Let $\xi_{n}=X_{n}-X_{n-1}$ where $EX_{0}^{2}, \sum\limits_{m}E\xi_{m}^{2} < \infty$ then $X_{n} \to X_{\infty}-$a.s. and $L^{2}$

Expected value of function of Markov chain

Stopping time and its probability showing $\mathbb{P}(\exists n \in \mathbb{N}_{0} : \sum_{k=1}^{n}V_{k} > a) \leq e^{-\lambda a}$

$P_{ij}=0$ if state $i$ is recurrent and it does not communicate with $j$

Show $\lim\limits_{\delta \to 0} E(\vert F((X_{t_{i}}+t_{i}B_{1})_{1 \leq i \leq n})-F(X)\vert A_{\delta}]=0$

Is expectation of an Ito integral always 0, regardless of the limits?

Time homogeneity and Markov property

$E(X_1X_2X_3X_4)\leq E(X_i^4)$ for some $i\in\{1,2,3,4\}$?

Find expectation $ E[S]$

Showing that $M_{\tau}$ and $M_{\tau \land n}$ are integrable

Prove that the Markov chain is irreducible and recurrent

If a process is 0 up to a stopping time, then the ito integral up to the stopping time is 0.

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