Question

How can we prove that $\inf\left\{t\in[0,T]:X_t\ge n\right\}\wedge T\xrightarrow{n\to\infty}T$, if $\operatorname P[X_T<\infty]=1$?

score 57 · Answer 1 · 2016-10-24 16:13:02

57

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How can we prove that $\inf\left\{t\in[0,T]:X_t\ge n\right\}\wedge T\xrightarrow{n\to\infty}T$, if $\operatorname P[X_T<\infty]=1$?

Published on 24 Oct 2016 - 16:13

score 266 · Answer 2 · 2016-10-25 13:30:42

266

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Martingale Rademacher exercise

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score 101 · Answer 3 · 2016-10-25 14:53:59

101

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Published on 25 Oct 2016 - 14:53

score 106 · Answer 4 · 2016-10-25 18:14:17

106

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Extension of the stochastic integral in the book "PDE and Martingale Methods in Option Pricing"

Published on 25 Oct 2016 - 18:14

score 298 · Answer 5 · 2016-10-25 21:58:12

298

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score 6k · Answer 6 · 2016-10-26 21:58:54

6k

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score 83 · Answer 7 · 2016-10-27 21:08:04

83

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score 269 · Answer 8 · 2026-02-23 08:28:25

269

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If $M$ is a local martingale and $τ_k^n$ is a stopping time, then $t↦\sum_{k∈ℕ}M_{τ_{k-1}^n}\left(M_{τ_k^n∧t}-M_{τ_{k-1}^n∧t}\right)$ is a martingale

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score 135 · Answer 9 · 2016-11-01 00:41:15

135

Views

Question to a proof about hitting and first return times

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score 66 · Answer 10 · 2016-11-04 22:25:38

66

Views

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Published on 04 Nov 2016 - 22:25

score 33 · Answer 11 · 2016-11-05 13:06:59

33

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Published on 05 Nov 2016 - 13:06

score 52 · Answer 12 · 2016-11-16 14:48:41

52

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score 87 · Answer 13 · 2016-11-17 17:54:00

87

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Published on 17 Nov 2016 - 17:54

score 1.6k · Answer 14 · 2016-11-17 19:23:04

1.6k

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Published on 17 Nov 2016 - 19:23

score 586 · Answer 15 · 2016-11-18 19:44:14

586

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Published on 18 Nov 2016 - 19:44

List Question

How can we prove that $\inf\left\{t\in[0,T]:X_t\ge n\right\}\wedge T\xrightarrow{n\to\infty}T$, if $\operatorname P[X_T<\infty]=1$?

Martingale Rademacher exercise

Prove that $\inf\left\{t\ge 0:Y_t=y\right\}$ is a stopping time

Extension of the stochastic integral in the book "PDE and Martingale Methods in Option Pricing"

Simple martingale question: expected stopping time for drunken walk

Prove that expectation of a stopping time is (in)finite

Double random hitting time with random barrier

If $M$ is a local martingale and $τ_k^n$ is a stopping time, then $t↦\sum_{k∈ℕ}M_{τ_{k-1}^n}\left(M_{τ_k^n∧t}-M_{τ_{k-1}^n∧t}\right)$ is a martingale

Question to a proof about hitting and first return times

Constructing a nearly 0 stochastic process or stopping times

Is it random variable?

A simple proof concerning stopping time - stochastic processes.

Passage probabilities for lines

Squared hitting time expectation including Brownian motion

Stopping time Independent random variables

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