Question

Distribution of first jump time

score 54 · Answer 1 · 2022-03-16 10:20:03

54

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Distribution of first jump time

Published on 16 Mar 2022 - 10:20

score 41 · Answer 2 · 2022-03-16 15:33:18

41

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Is the reciprocal of Lévy-Khintchine theorem for Levy process true?

Published on 16 Mar 2022 - 15:33

score 97 · Answer 3 · 2022-03-18 17:09:21

97

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Show that $\sum_{\substack{s\ge0\\\Delta X_s\ne0}}1_B(s,\Delta X_s)$ is measurable

Published on 18 Mar 2022 - 17:09

score 26 · Answer 4 · 2022-03-22 15:10:43

26

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

Published on 22 Mar 2022 - 15:10

score 18 · Answer 5 · 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 68 · Answer 6 · 2022-03-24 19:44:07

68

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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 24 Mar 2022 - 19:44

score 75 · Answer 7 · 2022-03-24 21:21:54

75

Views

Creeping for a Levy processes with infinite total mass

Published on 24 Mar 2022 - 21:21

score 44 · Answer 8 · 2026-03-26 14:34:50

44

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If $M,N$ are martingales, show that $\operatorname E\left[M_tN_t\right]=\operatorname E\left[\sum_{s\in(0,\:t]}\Delta M_s\Delta N_s\right]$

Published on 26 Mar 2026 - 14:34

score 97 · Answer 9 · 2022-03-29 16:34:19

97

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Bound for the probability of a Lévy process having a jump of a given size

Published on 29 Mar 2022 - 16:34

score 102 · Answer 10 · 2022-03-29 16:43:02

102

Views

Is the limit in probability of Lévy processes still a Lévy process?

Published on 29 Mar 2022 - 16:43

score 29 · Answer 11 · 2022-03-31 16:08:16

29

Views

Is the jump measure of a space homogeneous Markov process translation invariant?

Published on 31 Mar 2022 - 16:08

score 29 · Answer 12 · 2022-04-05 09:12:09

29

Views

If $X$ is a Lévy process, then $\operatorname{Var}[X_n]=n\operatorname{Var}[X_1]$

Published on 05 Apr 2022 - 9:12

score 207 · Answer 13 · 2026-02-23 15:12:31

207

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Show that every continuous Lévy process is a Wiener process

Published on 23 Feb 2026 - 15:12

score 25 · Answer 14 · 2022-04-10 07:41:07

25

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Does $\int\min(1,\|x\|)<\infty$ imply $\int\left|e^{{\rm i}\langle x,\:x'\rangle}-1-{\rm i}\langle x,x'\rangle1_{\overline B_1(0)}(x)\right|<\infty$

Published on 10 Apr 2022 - 7:41

score 193 · Answer 15 · 2022-04-11 08:21:59

193

Views

Jumps of a compound Poisson process

Published on 11 Apr 2022 - 8:21

List Question

Distribution of first jump time

Is the reciprocal of Lévy-Khintchine theorem for Levy process true?

Show that $\sum_{\substack{s\ge0\\\Delta X_s\ne0}}1_B(s,\Delta X_s)$ is measurable

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

Creeping for a Levy processes with infinite total mass

If $M,N$ are martingales, show that $\operatorname E\left[M_tN_t\right]=\operatorname E\left[\sum_{s\in(0,\:t]}\Delta M_s\Delta N_s\right]$

Bound for the probability of a Lévy process having a jump of a given size

Is the limit in probability of Lévy processes still a Lévy process?

Is the jump measure of a space homogeneous Markov process translation invariant?

If $X$ is a Lévy process, then $\operatorname{Var}[X_n]=n\operatorname{Var}[X_1]$

Show that every continuous Lévy process is a Wiener process

Does $\int\min(1,\|x\|)<\infty$ imply $\int\left|e^{{\rm i}\langle x,\:x'\rangle}-1-{\rm i}\langle x,x'\rangle1_{\overline B_1(0)}(x)\right|<\infty$

Jumps of a compound Poisson process

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