Question

On the continuity of the product of a left-continuous and a right-continuous stochastic process

score 70 · Answer 1 · 2026-04-01 15:08:56

70

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On the continuity of the product of a left-continuous and a right-continuous stochastic process

Published on 01 Apr 2026 - 15:08

score 105 · Answer 2 · 2026-03-27 04:21:50

105

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Karatzas + Shreve 2.22: For optional time $S$, stopping time $T$, prove that $\mathscr{F}_{S+} \subset \mathscr{F}_T$

Published on 27 Mar 2026 - 4:21

score 27 · Answer 3 · 2026-03-27 17:24:24

27

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Show that the inter-jump times of a Lévy process are i.i.d.

Published on 27 Mar 2026 - 17:24

score 18 · Answer 4 · 2026-03-17 13:41:53

18

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If $r:=\operatorname{dist}(0,\overline B)$, what's the relation between $\{t>τ^B_{n-1}:\Delta x(t)\in B\}$ and $\{s\in(0,t]:\|\Delta x(s)\|_E\ge r\}$

Published on 17 Mar 2026 - 13:41

score 69 · Answer 5 · 2026-03-27 17:24:20

69

Views

If $\pi_t$ is the jump measure of a Lévy process and $B_1,\ldots,B_k$ are disjoint, then $\pi_t(B_1),\pi_t(B_k)$ are independent

Published on 27 Mar 2026 - 17:24

score 28 · Answer 6 · 2022-03-24 20:27:55

28

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Brownian motion & strong markov property

Published on 24 Mar 2022 - 20:27

score 83 · Answer 7 · 2026-03-27 04:23:51

83

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Given sequence of optional times $T_n$ and optional time $T = \inf_n T_n$, show $\mathscr{F}_{T+} = \cap_n \mathscr{F}_{T_n+}$

Published on 27 Mar 2026 - 4:23

score 36 · Answer 8 · 2026-03-27 04:23:49

36

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With optional time $T$ on $\mathscr{F}_t$, and $T_n = \frac{k}{2^n}$ on $\{ \frac{k-1}{2^n} \le T < \frac{k}{2^n} \}$, show $T_n$ is a stopping time

Published on 27 Mar 2026 - 4:23

score 192 · Answer 9 · 2026-03-29 23:35:40

192

Views

M($\lambda$)/M($\mu$)/n queue, recurrence and busy periods

Published on 29 Mar 2026 - 23:35

score 73 · Answer 10 · 2026-03-28 01:18:47

73

Views

Finding the expectation of a stopping time

Published on 28 Mar 2026 - 1:18

score 147 · Answer 11 · 2022-04-11 15:58:01

147

Views

Brownian Motion hitting times in one dimension

Published on 11 Apr 2022 - 15:58

score 396 · Answer 12 · 2022-04-11 19:40:51

396

Views

Expected value of minimum of hitting time of brownian motion.

Published on 11 Apr 2022 - 19:40

score 156 · Answer 13 · 2022-04-13 01:06:57

156

Views

On a Stopping Time Argument in Harmonic Analysis

Published on 13 Apr 2022 - 1:06

score 193 · Answer 14 · 2022-04-13 06:38:55

193

Views

Two "racing" sequences, what is the probability and expected stopping time that one will "catch up" to the other?

Published on 13 Apr 2022 - 6:38

score 64 · Answer 15 · 2022-04-13 21:29:32

64

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proof verification: problem 1.3.24 from Shreve and Karatzas ii

Published on 13 Apr 2022 - 21:29

List Question

On the continuity of the product of a left-continuous and a right-continuous stochastic process

Karatzas + Shreve 2.22: For optional time $S$, stopping time $T$, prove that $\mathscr{F}_{S+} \subset \mathscr{F}_T$

Show that the inter-jump times of a Lévy process are i.i.d.

If $r:=\operatorname{dist}(0,\overline B)$, what's the relation between $\{t>τ^B_{n-1}:\Delta x(t)\in B\}$ and $\{s\in(0,t]:\|\Delta x(s)\|_E\ge r\}$

If $\pi_t$ is the jump measure of a Lévy process and $B_1,\ldots,B_k$ are disjoint, then $\pi_t(B_1),\pi_t(B_k)$ are independent

Brownian motion & strong markov property

Given sequence of optional times $T_n$ and optional time $T = \inf_n T_n$, show $\mathscr{F}_{T+} = \cap_n \mathscr{F}_{T_n+}$

With optional time $T$ on $\mathscr{F}_t$, and $T_n = \frac{k}{2^n}$ on $\{ \frac{k-1}{2^n} \le T < \frac{k}{2^n} \}$, show $T_n$ is a stopping time

M($\lambda$)/M($\mu$)/n queue, recurrence and busy periods

Finding the expectation of a stopping time

Brownian Motion hitting times in one dimension

Expected value of minimum of hitting time of brownian motion.

On a Stopping Time Argument in Harmonic Analysis

Two "racing" sequences, what is the probability and expected stopping time that one will "catch up" to the other?

proof verification: problem 1.3.24 from Shreve and Karatzas ii

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