User Amira

4 votes

0 answers

183 views

Prove the following stopping time Cannot be a predictable stopping time.

asked Aug 19, 2019 at 23:12

4 votes

0 answers

87 views

Expectation of the exponential of the amount of time a Brownian motion spent in half space

asked Sep 15, 2022 at 14:00

4 votes

0 answers

141 views

Solving a PDE from the Feymann-Kac formula

asked May 11 at 2:13

3 votes

3 answers

156 views

Explicit solution for the expectation of inverse of the exponential of normal random variable

asked Apr 29 at 16:06

2 votes

0 answers

24 views

General solution for ''homogeneous and linear PDE''

asked Sep 25, 2022 at 21:29

2 votes

1 answer

90 views

Prove the equality $\mathbb{E}[(X_s^2-\mathbb{E}[X_s^2])(X_t^2-\mathbb{E}[X_t^2])]=2\mathbb{E}[X_sX_t]^2$

asked May 22, 2017 at 22:01

2 votes

0 answers

69 views

Stochastic exponential of a true martingale is also a true martingale?

asked Dec 3, 2020 at 19:09

2 votes

0 answers

38 views

Expectation of share of Geometric Brownian motions

asked Apr 14, 2021 at 11:20

2 votes

1 answer

152 views

Is the local time of the reflected SDE Markovian?

asked Jun 24, 2021 at 22:17

2 votes

0 answers

42 views

Coin toss: probability of "maximum difference between heads and tail not to exceed a boundary"

asked Feb 3, 2022 at 1:50

1 vote

0 answers

147 views

Comparison theorem for the following linear SDE

asked Dec 3, 2019 at 20:39

1 vote

0 answers

91 views

Extend $C^2$ functions while preserve its first derivative at the boundary

asked Dec 29, 2019 at 6:52

1 vote

1 answer

383 views

Prove $\mathrm{Cov}[f(X),g(Y)]^2\leq E[XY]^2\mathrm{Var}[f(X)]\mathrm{Var}[g(Y)]$ if $X$ and $Y$ are standard normal

asked Jun 21, 2017 at 19:49

1 vote

1 answer

169 views

Quotient of dY_t/d_X_t makes sense?

asked Dec 11, 2017 at 2:35

1 vote

0 answers

53 views

Compare expectations of two processes

asked Sep 10, 2019 at 20:35

1 vote

0 answers

162 views

A right-continuous non-decreasing process is cadlag?

asked Mar 4, 2019 at 20:38

1 vote

3 answers

51 views

Simplification of proof for $\exists c>0$ such that $|x+y|\leq c(1+\sqrt{x^2+y^2})$

asked Jun 10, 2019 at 14:37

1 vote

0 answers

89 views

Uniqueness for autonomous ODE with discontinuous coefficient

asked Jun 22, 2019 at 0:05

1 vote

0 answers

58 views

Conditional expectation of the exponential of the integral of a diffusion

asked Sep 28, 2022 at 8:42

1 vote

1 answer

111 views

Can any càdlàg function be decoomposed into a continuous part and a discontinuous part?

asked Feb 22 at 11:32

1 vote

1 answer

48 views

$\lim_{y\downarrow 0}F\left(f(y),y\right)=\lim_{y\downarrow 0}F(\lim_{\tilde y\downarrow 0}f(\tilde y),y)?$ [closed]

asked Oct 9, 2020 at 10:15

1 vote

0 answers

76 views

Expectation of the exponential of the sum of Brownian motion and the time it spent above certain threshold

asked Sep 20, 2022 at 15:48

0 votes

1 answer

20 views

Doob-Meyer decomposition of number of times the diffusion cross a barrier

asked Sep 20, 2022 at 13:08

0 votes

2 answers

59 views

Does $f\in L^2(\mathbb{R}^p) $ imply $ f(\cdot , x) \in L^2(\mathbb{R}^{p-1})$?(answered) [closed]

asked Mar 20, 2017 at 21:35

0 votes

0 answers

62 views

Natural filtration of a Markov process

asked Sep 30, 2019 at 18:22

0 votes

0 answers

29 views

Calculating expectation by change of probability measure

asked May 5 at 21:07

0 votes

0 answers

30 views

Three exponential random variables, given the correlations of two pairs, what is the correlation for the third pair?

asked Jun 25 at 9:15

0 votes

1 answer

571 views

Intersection of two independent sigma-algebras is trivial sigma-algebra?

asked Mar 3, 2019 at 20:54

0 votes

1 answer

25 views

Compare the limit of a sequence with the upper bound of the sequence as in Dominated convergence theorem

asked Jan 9, 2020 at 14:58

0 votes

3 answers

437 views

Find the 'best' upper bound

asked Jan 22, 2020 at 20:42

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34 Questions

Prove the following stopping time Cannot be a predictable stopping time.

Expectation of the exponential of the amount of time a Brownian motion spent in half space

Solving a PDE from the Feymann-Kac formula

Explicit solution for the expectation of inverse of the exponential of normal random variable

General solution for ''homogeneous and linear PDE''

Prove the equality $\mathbb{E}[(X_s^2-\mathbb{E}[X_s^2])(X_t^2-\mathbb{E}[X_t^2])]=2\mathbb{E}[X_sX_t]^2$

Stochastic exponential of a true martingale is also a true martingale?

Expectation of share of Geometric Brownian motions

Is the local time of the reflected SDE Markovian?

Coin toss: probability of "maximum difference between heads and tail not to exceed a boundary"

Comparison theorem for the following linear SDE

Extend $C^2$ functions while preserve its first derivative at the boundary

Prove $\mathrm{Cov}[f(X),g(Y)]^2\leq E[XY]^2\mathrm{Var}[f(X)]\mathrm{Var}[g(Y)]$ if $X$ and $Y$ are standard normal

Quotient of dY_t/d_X_t makes sense?

Compare expectations of two processes

A right-continuous non-decreasing process is cadlag?

Simplification of proof for $\exists c>0$ such that $|x+y|\leq c(1+\sqrt{x^2+y^2})$

Uniqueness for autonomous ODE with discontinuous coefficient

Conditional expectation of the exponential of the integral of a diffusion

Can any càdlàg function be decoomposed into a continuous part and a discontinuous part?

$\lim_{y\downarrow 0}F\left(f(y),y\right)=\lim_{y\downarrow 0}F(\lim_{\tilde y\downarrow 0}f(\tilde y),y)?$ [closed]

Expectation of the exponential of the sum of Brownian motion and the time it spent above certain threshold

Doob-Meyer decomposition of number of times the diffusion cross a barrier

Does $f\in L^2(\mathbb{R}^p) $ imply $ f(\cdot , x) \in L^2(\mathbb{R}^{p-1})$?(answered) [closed]

Natural filtration of a Markov process

Calculating expectation by change of probability measure

Three exponential random variables, given the correlations of two pairs, what is the correlation for the third pair?

Intersection of two independent sigma-algebras is trivial sigma-algebra?

Compare the limit of a sequence with the upper bound of the sequence as in Dominated convergence theorem

Find the 'best' upper bound