User Paul - Mathematics Stack Exchange

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	335 reputation	bio	website		visits	member for	11 months
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2

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0

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46

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Proving that $ \int \left| f-g \right|~d\mu = 2\int_{A_0} (f-g)~d\mu$

measure-theory probability-theory

may 15 at 16:33 Paul 335

2

votes

0

answers

58

views

Gaussian vectors formula

probability-theory

may 13 at 11:02 Paul 335

2

votes

1

answer

50

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Reality check: $\mathbb E \{ B_s B_t ^2\}=0 $

probability-theory stochastic-processes

apr 15 at 19:51 Did 103k

1

vote

2

answers

85

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Conditional expectation of a functional of an Itô's semimartingale under its equivalent martingale measure

probability-theory stochastic-processes stochastic-calculus stochastic-integrals

apr 18 at 17:51 Paul 335

0

votes

0

answers

27

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Non-arbitrage theory and existence of a risk premium

probability-theory stochastic-processes finance

apr 8 at 21:35 Paul 335

6

votes

1

answer

112

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Very basic doubt about Itô's lemma

probability-theory stochastic-processes stochastic-calculus stochastic-integrals

mar 19 at 11:59 Ilya 14.2k

2

votes

1

answer

57

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Dirac function and integration by parts

integral integration normal-distribution distribution-theory

feb 15 at 1:22 joriki 92.6k

1

4

votes

1

answer

65

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Upper bound concerning Snell envelope

probability-theory stochastic-processes stochastic-calculus control-theory

feb 14 at 16:47 Ilya 14.2k

1

vote

1

answer

31

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Why $\mathbb E \left[ \exp (u X_t )\right] < \infty$ if and only if $\int_{|z|>1} e^{uz} ~\nu(dz) < \infty$ for a Lévy process?

probability-theory stochastic-processes stochastic-calculus

feb 1 at 15:46 Did 103k

1

vote

1

answer

103

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Show that $Z_t = Z_0 \exp\left( \mu t + X_t \right)$ is well defined where $X_t$ is a Jump process (Lévy process)

probability-theory stochastic-processes stochastic-calculus random-walk

feb 1 at 7:59 Did 103k

2

votes

1

answer

53

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Continuous local martingales with same crochet have the same law?

probability-theory stochastic-processes stochastic-calculus

jan 19 at 12:10 Ju'x 2,934

1

vote

1

answer

65

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Asymptotic Behaviour of a Continuous Square Integrable Martingale

probability-theory stochastic-processes convergence stochastic-calculus martingales

jan 18 at 22:21 Ju'x 2,934

2

votes

1

answer

78

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About stochastic differential equations

probability-theory stochastic-processes stochastic-calculus stochastic-integrals

jan 18 at 22:07 Ju'x 2,934

0

votes

1

answer

107

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About exponential martingales

stochastic-processes stochastic-calculus

2d ago Byron Schmuland 15.4k

0

votes

1

answer

41

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Conditional law of $X_t | Y_t$ of the Gaussian stochastic process $Z_t=\left( X_t, Y_t\right)$

probability-theory stochastic-processes stochastic-calculus

jan 17 at 21:13 Sasha 41.4k

4

votes

2

answers

45

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Show $ \int _0^t \frac{\left|B_u \right|}{u}du < \infty \ a.e.$

stochastic-processes stochastic-calculus

jan 16 at 13:36 Ju'x 2,934

4

11

votes

3

answers

283

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Limit of a Wiener integral

probability-theory stochastic-processes stochastic-calculus stochastic-integrals

jan 19 at 8:02 Did 103k

1

3

votes

1

answer

118

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About stopping times and progressively measurable process

probability-theory stochastic-processes stochastic-calculus

jan 16 at 12:20 Paul 335

0

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1

answer

30

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How can we easily compute $\mathbb{E} [ \left|W_t\right| ^\alpha]$?

stochastic-processes brownian-motion

jan 14 at 16:10 Did 103k

0

votes

1

answer

77

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How to show that $X_t = \frac{1}{\left| B_t -x\right|}\mathbb{1}_{\left\{ B_t \neq x\right\}}$ (“inverse brownian”) is a martingale?

probability-theory stochastic-processes brownian-motion martingales

jan 5 at 18:00 Did 103k

1

vote

1

answer

48

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Covariation of a gaussian process $ G_t = \int_0 ^t \frac{B_u}{u}du$

probability-theory stochastic-processes

jan 4 at 13:10 Did 103k

2

votes

1

answer

71

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Show that $M_t = \int_0 ^t \exp{((B_2(s)^2)} dB_1(s)$ is not a continuous square integrable martingale

probability-theory stochastic-processes brownian-motion

jan 4 at 14:09 Did 103k

3

votes

1

answer

87

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What is the law of the ratio of two independent gaussian randon variables? [duplicate]

probability probability-theory

jan 1 at 19:48 Michael Hardy 48.1k

6

votes

3

answers

287

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What is the probability that the center of the circle is contained within the triangle?

probability circle geometric-probability

jan 17 at 21:47 joriki 92.6k

1

5

votes

5

answers

132

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Smart demonstration to the formula $ \sum_{n=1} ^{N} \frac{n}{2^n} = \frac{-N + 2^{N+1}-2}{2^n}$

sequences-and-series

jan 3 at 13:34 Tim Monahan 271

3

votes

1

answer

167

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Funny problem about stochastic integrals and Ito' s lemma

probability stochastic-processes stochastic-calculus stochastic-integrals

dec 31 at 11:00 TheBridge 1,506

0

votes

2

answers

136

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Explicit solution of a SDE

probability stochastic-processes stochastic-calculus stochastic-integrals

jan 4 at 11:12 saz 5,457

1

vote

1

answer

83

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Upper bound for the $\sup$ of a martingale defined as a stochastic integral of a general continuous martingale

probability stochastic-processes stochastic-calculus stochastic-integrals

jan 1 at 15:04 Paul 335

1

vote

1

answer

52

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Explicit solution of a SDE envolving a probability measure changing

probability-theory stochastic-processes

dec 31 at 12:50 TheBridge 1,506

1

vote

1

answer

132

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The law of absolute value of a standard Brownian motion

probability probability-theory stochastic-processes

dec 29 at 4:32 adam W 3,180

Paul

32 Questions