List questions from stochastic-processes

Published on 16 Apr 2026 - 7:32

107

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Show that $\operatorname P\left[\sup_{s\in[0,\:t]}\left(M_s-\frac\alpha2[M]_s\right)\ge\alpha\beta\right]\le e^{-\alpha\beta}$

Published on 16 Apr 2026 - 21:01

18

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Expecation of $S(t)=\sum_{i=1}^{N(t)}(X_i+T_i)^2$ for Poisson process $N(t)$

Published on 16 Apr 2026 - 8:20

395

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Wiener integral as a special case of Ito integral

Published on 12 Apr 2026 - 13:28

440

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Expected value and variance of a stopping time

Published on 14 Apr 2026 - 5:16

98

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(Feller Vol.1) the generating function for the probabilities that the event $S_n = r$ will occur exactly $k$ times

Published on 15 Apr 2026 - 14:45

55

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Example of Markov process not having transition density function

Published on 13 Apr 2026 - 22:11

47

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Can you give me some clue on proofing that squared log-returns of a GARCH(1,1) time series is ARMA(1,1)?

Published on 15 Apr 2026 - 8:25

133

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Expectation of reaching state from transition matrix

Published on 11 Apr 2026 - 13:20

623

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Proof that the jump measure of a Lévy process is a Poisson random measure

Published on 26 Mar 2026 - 6:21

179

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What is the popular way to simulate an Ito process?

Published on 10 Apr 2026 - 14:14

167

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Strategy to beat the casino with unlimited amount of money (Martingales)

Published on 25 Mar 2026 - 19:07

56

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If $f$ is nice what is $E[f(B(t)) \mid \mathcal F_s]$ for $s\leq t$?

Published on 15 Apr 2026 - 21:55

83

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Inverse law of large numbers for groups?

Published on 12 Apr 2026 - 22:28

1k

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uniform integrability of all conditional expectations of a fixed $L^1$ function

Published on 15 Apr 2026 - 2:54

List Question

Auxiliary result related to the exponential martingale inequality

Show that $\operatorname P\left[\sup_{s\in[0,\:t]}\left(M_s-\frac\alpha2[M]_s\right)\ge\alpha\beta\right]\le e^{-\alpha\beta}$

Expecation of $S(t)=\sum_{i=1}^{N(t)}(X_i+T_i)^2$ for Poisson process $N(t)$

Wiener integral as a special case of Ito integral

Expected value and variance of a stopping time

(Feller Vol.1) the generating function for the probabilities that the event $S_n = r$ will occur exactly $k$ times

Example of Markov process not having transition density function

Can you give me some clue on proofing that squared log-returns of a GARCH(1,1) time series is ARMA(1,1)?

Expectation of reaching state from transition matrix

Proof that the jump measure of a Lévy process is a Poisson random measure

What is the popular way to simulate an Ito process?

Strategy to beat the casino with unlimited amount of money (Martingales)

If $f$ is nice what is $E[f(B(t)) \mid \mathcal F_s]$ for $s\leq t$?

Inverse law of large numbers for groups?

uniform integrability of all conditional expectations of a fixed $L^1$ function

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