Question

If a càdlàg function $x$ has a jump $\Delta x(t)$ of magnitude $\ge r$, then $\|x(s)-x(u)\|\ge r$ for all $t-\delta\le s\le t\le u<t+\delta$

score 61 · Answer 1 · 2021-10-31 15:34:25

61

Views

If a càdlàg function $x$ has a jump $\Delta x(t)$ of magnitude $\ge r$, then $\|x(s)-x(u)\|\ge r$ for all $t-\delta\le s\le t\le u<t+\delta$

Published on 31 Oct 2021 - 15:34

score 80 · Answer 2 · 2021-11-01 11:11:22

80

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How do we see that the jump time of a Lévy process is exponentially distributed using the Markov property?

Published on 01 Nov 2021 - 11:11

score 224 · Answer 3 · 2021-11-21 20:26:21

224

Views

If $\tau$ is a stopping time with $\text P[\tau>s+t]=\text P[\tau>s]\text P[\tau>t]$, how do we determine the rate of the exponential distribution?

Published on 21 Nov 2021 - 20:26

score 19 · Answer 4 · 2026-03-24 07:15:43

19

Views

Solution of a special case of Lèvy flight

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score 74 · Answer 5 · 2021-12-12 19:06:14

74

Views

How to interpret the cartesian product of Borel sets, $\mathcal B[0,∞)\times \mathcal B(\Bbb R \setminus \{0\})$?

Published on 12 Dec 2021 - 19:06

score 126 · Answer 6 · 2021-12-22 20:58:54

126

Views

Prove that $N(t,A):=\left|\left\{s\in(0,t]:\Delta X(s)\in A\right\}\right|$ has independent increments

Published on 22 Dec 2021 - 20:58

score 605 · Answer 7 · 2022-01-03 12:55:41

605

Views

Combining the derivative of two Brownian motions into one.

Published on 03 Jan 2022 - 12:55

score 209 · Answer 8 · 2022-01-05 19:12:54

209

Views

Can a stochastic process have stationary increments which are not independent increments?

Published on 05 Jan 2022 - 19:12

score 209 · Answer 9 · 2022-01-24 18:35:29

209

Views

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Published on 24 Jan 2022 - 18:35

score 100 · Answer 10 · 2022-02-03 09:57:49

100

Views

Theorem Sato 30.1 subordinated levy process

Published on 03 Feb 2022 - 9:57

score 515 · Answer 11 · 2022-02-04 15:42:19

515

Views

Numerical simulation of SDE's driven by Lévy processes (particularly stable processes)

Published on 04 Feb 2022 - 15:42

score 38 · Answer 12 · 2026-03-26 23:11:27

38

Views

Intersection of random fractals; i.e. the range of $\alpha$-stable subordinators

Published on 26 Mar 2026 - 23:11

score 596 · Answer 13 · 2022-02-26 02:36:27

596

Views

An application of Ito lemma for Ito-Levy processes

Published on 26 Feb 2022 - 2:36

score 132 · Answer 14 · 2022-03-05 12:58:37

132

Views

How can we show that the jump measure of a càdlàg process is a counting measure?

Published on 05 Mar 2022 - 12:58

score 370 · Answer 15 · 2026-03-26 03:00:53

370

Views

Numerical simulation of SDE with Lévy noise in Python - Overflow issue

Published on 26 Mar 2026 - 3:00

List Question

If a càdlàg function $x$ has a jump $\Delta x(t)$ of magnitude $\ge r$, then $\|x(s)-x(u)\|\ge r$ for all $t-\delta\le s\le t\le u<t+\delta$

How do we see that the jump time of a Lévy process is exponentially distributed using the Markov property?

If $\tau$ is a stopping time with $\text P[\tau>s+t]=\text P[\tau>s]\text P[\tau>t]$, how do we determine the rate of the exponential distribution?

Solution of a special case of Lèvy flight

How to interpret the cartesian product of Borel sets, $\mathcal B[0,∞)\times \mathcal B(\Bbb R \setminus \{0\})$?

Prove that $N(t,A):=\left|\left\{s\in(0,t]:\Delta X(s)\in A\right\}\right|$ has independent increments

Combining the derivative of two Brownian motions into one.

Can a stochastic process have stationary increments which are not independent increments?

A question about the Lévy-Khintchine formula

Theorem Sato 30.1 subordinated levy process

Numerical simulation of SDE's driven by Lévy processes (particularly stable processes)

Intersection of random fractals; i.e. the range of $\alpha$-stable subordinators

An application of Ito lemma for Ito-Levy processes

How can we show that the jump measure of a càdlàg process is a counting measure?

Numerical simulation of SDE with Lévy noise in Python - Overflow issue

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