List questions from stopping-times

710

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If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

Published on 14 Dec 2018 - 16:44

1.3k

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The distribution of a stopping time

Published on 28 Dec 2018 - 19:00

1.2k

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Show a Continuous Local Martingale is a Martingale

Published on 31 Dec 2018 - 16:23

440

Views

Expected value of Brownian motion at a time decided by a rate one Poisson process.

Published on 31 Dec 2018 - 17:23

630

Views

Finding expected value of a stopping time dependent on a Poisson process and a variable $n$

Published on 02 Jan 2019 - 18:55

89

Views

Compute $E(M_σ)$ when $σ = \inf(t ≥ 0: |B_t| = 1)$ and $M_t = 4B^2_t +e^{4B_t−8t}−4t$

Published on 06 Jan 2019 - 11:44

143

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Bounding expectation of stopping time

Published on 07 Jan 2019 - 22:56

412

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Proving that stopping time is finite a.s.

Published on 08 Jan 2019 - 21:03

117

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Standard Brownian motion and stopping time

Published on 11 Jan 2019 - 20:34

121

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Intersection-exponent for one-dimensional Brownian motion

Published on 18 Jan 2019 - 12:49

4.9k

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Collection: Results on stopping times for Brownian motion (with drift)

Published on 19 Jan 2019 - 11:06

210

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Convergence of $\sigma-$algebra for converging stopping time

Published on 20 Jan 2019 - 9:15

669

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Cauchy density function for Brownian motion

Published on 21 Jan 2019 - 16:30

1k

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Conditional expectation for Brownian motion

Published on 21 Jan 2019 - 20:53

556

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Conditional expectation of Brownian motion given stopping-time sigma algebra

Published on 23 Jan 2019 - 15:11

List Question

If $\tau=\inf \{t \ge 0: B(t)= -a \text{ or } b\}$ is a stopping time of Brownian motion $B_t$, why does $E(\tau)=E(B_{\tau}^2)$?

The distribution of a stopping time

Show a Continuous Local Martingale is a Martingale

Expected value of Brownian motion at a time decided by a rate one Poisson process.

Finding expected value of a stopping time dependent on a Poisson process and a variable $n$

Compute $E(M_σ)$ when $σ = \inf(t ≥ 0: |B_t| = 1)$ and $M_t = 4B^2_t +e^{4B_t−8t}−4t$

Bounding expectation of stopping time

Proving that stopping time is finite a.s.

Standard Brownian motion and stopping time

Intersection-exponent for one-dimensional Brownian motion

Collection: Results on stopping times for Brownian motion (with drift)

Convergence of $\sigma-$algebra for converging stopping time

Cauchy density function for Brownian motion

Conditional expectation for Brownian motion

Conditional expectation of Brownian motion given stopping-time sigma algebra

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