User Nicolas Essis-Breton - Mathematics Stack Exchange

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	1,350 reputation	bio	website	neblink.wordpress.com	visits	member for	1 year, 9 months
313 badges		location	Montreal, Canada		seen	10 hours ago

3

votes

2

answers

295

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Irreducible and aperiodic Markov chain : $P^t(x,y)>0$

markov-chains

sep 14 '11 at 20:04 Srivatsan 15.6k

2

votes

1

answer

34

views

Show $5z^n=e^z$ has a finite number of zero in $\{a<\Im z < v\}$ and $\{a < \Re z < b \}$

complex-analysis

may 17 at 4:53 75064 2,030

2

votes

1

answer

53

views

Probabilistic calulation of the Fourier transform of the Cantor function

may 3 at 15:20 MichaelNgelo 180

2

votes

0

answers

29

views

Is it possible to construct a Loeb measure for $\{\epsilon: \epsilon\in[0,1], \epsilon \text{ infinitesimal}\}$?

nonstandard-analysis

apr 22 at 15:52 Michael Hardy 47.9k

2

votes

2

answers

37

views

If $\dim(A+B)=\dim(A\cap B)+1$, then $A \subset B$ or $B \subset A$

linear-algebra vector-spaces

apr 10 at 18:15 julien 22.5k

2

votes

3

answers

94

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$d\left(\left(x_1,x_2\right),\left(y_1,y_2\right)\right)=|x_1-x_2|+|x_1-y_1|+|y_1-y_2|$ : complete?

metric-spaces

feb 11 at 9:27 Brian M. Scott 154k

1

2

votes

2

answers

62

views

$f$ continuous on a circle, then there is a diameter at which ends $f$ has the same value

real-analysis complex-analysis

feb 8 at 21:59 oxeimon 189

2

votes

1

answer

46

views

$A$ skew-symmetric, then $x^T A^2 x \le 0$

linear-algebra

feb 7 at 19:38 user7530 8,218

2

votes

0

answers

30

views

If $a_n-c_{n,m} + a_m - c_{n,m} \xrightarrow{n,m} 0$, does $\{a_n\}$ and $\{c_{n,m}\}$ converge?

real-analysis

feb 3 at 2:36 vonbrand 6,548

1

2

votes

1

answer

51

views

Levy process : $E\left[\exp\left(\theta^X_\tau -\Psi(\theta^)\tau\right)1_{\{\tau < \infty\}}\right] = e^{\theta^*x}P\left( \tau < \infty \right)$

probability-theory stochastic-processes

jan 18 at 21:14 Did 102k

2

votes

0

answers

71

views

Solved problems book in Mathematical statistics

reference-request statistics

nov 16 at 2:27 Nicolas Essis-Breton 1,350

2

votes

1

answer

107

views

Quadratic variation of $X_t=\int_0^t B_s \, ds$

brownian-motion stochastic-integrals stochastic-calculus

nov 14 at 0:45 Michael Hardy 47.9k

1

2

votes

1

answer

262

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Show smooth functions of compact support are dense in the Schwartz space

functional-analysis fourier-analysis

nov 11 at 16:28 Matt N. 15.2k

2

votes

2

answers

81

views

Second order linear partial differential equation: $\partial_t u(t,x)+\frac12 \partial_{x,x} u(t,x)+u(t,x)v(x)=0$

pde brownian-motion stochastic-calculus stochastic-analysis

nov 6 at 22:29 doraemonpaul 3,021

2

votes

1

answer

134

views

Fourier transform of the Cantor function

measure-theory fourier-analysis

oct 25 at 0:23 sos440 13.9k

2

votes

1

answer

94

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Derivating $f(t)=\int_0^t x dx$ using measure theory

analysis measure-theory

oct 16 at 20:27 kahen 8,054

2

votes

1

answer

114

views

Convergence of the Fourier series of $f(t)=(t-\pi)\chi_{\left(0,2\pi\right)}$

fourier-analysis fourier-series

oct 16 at 7:15 Willie Wong♦ 30.6k

2

votes

1

answer

91

views

Show translation is not continuous in $\text{Lip}_\alpha(T)$

measure-theory fourier-analysis

sep 25 at 3:19 Community♦ 1

2

votes

1

answer

84

views

Find $\displaystyle{\int_C \left(1+ \frac{2}{z}\right) dz}$ , where $C(\theta)= e^{i\theta}, 0 \le \theta \le \pi$

complex-analysis

aug 29 at 2:46 DonAntonio 46.3k

2

votes

2

answers

45

views

Show $f(x)=\int_E x^tg(t)d\mu(t)$ is continuous when $\mu$ is a general measure

measure-theory

jun 19 '12 at 18:39 Byron Schmuland 15.4k

2

votes

1

answer

80

views

Show $f \in L^p$ implies there is a set $E$ and a function $g$ for which $f=f\chi_E+g$ with $m(E)<\infty$ and $|g|\le 1$

measure-theory

apr 11 '12 at 19:50 Nicolas Essis-Breton 1,350

2

votes

1

answer

446

views

Show a function is continuous if and only if it is both upper and lower semi-continuous

real-analysis analysis measure-theory

feb 18 '12 at 0:16 Michael Hardy 47.9k

2

votes

1

answer

60

views

Random walk on connected graph: show $E_vT_w \ne E_wT_v$

markov-chains

nov 14 '11 at 20:22 Mike Spivey 25.8k

2

votes

1

answer

234

views

Total variation distance and mutually singular probability measure

measure-theory

oct 8 '11 at 8:06 Ilya 14.2k

2

votes

1

answer

94

views

Branching process: show $P(Z_m>k|Z_n=0) \le (G_n(0))^k, m<n,k\ge 0$

probability

oct 4 '11 at 22:04 Did 102k

1

vote

1

answer

21

views

Mean number of particle present in the system: birth-death process, $E(X_t|X_0=i)$, $b_i=\frac{b}{i+1}$, $d_i=d$

probability-theory markov-chains queueing-theory

may 13 at 7:48 Did 102k

1

vote

0

answers

27

views

Maximum likelihood in exponential family: $\partial_{\theta,\theta} \ln L = -\mathrm{Var}(T)$, $T$ sufficient for $\theta$

statistics probability-theory

may 12 at 17:57 Nicolas Essis-Breton 1,350

1

vote

1

answer

35

views

Show $\dbinom{n}{2}^{-1} \sum_{i < j} X_i X_j \xrightarrow{p} \mu^2$, when $X_i$ are i.i.d. with mean $\mu$ and finite variance

probability-theory convergence limit-theorems

may 5 at 19:56 Did 102k

1

vote

1

answer

28

views

$X_n \sim \text{Exponential}(\lambda_n)$, independent, $\sum 1/\lambda_n = \infty$, then, $\sum X_n=\infty$ a.s.

probability-theory convergence random-variables

apr 29 at 20:04 Davide Giraudo 56.1k

1

vote

2

answers

21

views

Show $\det \left[T\right]_\beta=-1$, for any basis $\beta$ when $Tx=x-2(x,u)u$, $u$ unit vector

linear-algebra

apr 23 at 14:28 Michael Joyce 7,058

Nicolas Essis-Breton

129 Questions