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charlus
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4 votes

Complicated Improper Integral convergence/divergence

4 votes
Accepted

Proof : Given a finite set of equidimensional proper subspaces of a vector space $V$, $\exists$ $x$ in $V$ that belongs to none of them

4 votes
Accepted

Conditional expectations of $X$ with respect to a filtration converges to $X$

3 votes

Limit of a martingale sequence

3 votes

Variance of a series of IID's vs a multiple of a random variable

2 votes
Accepted

Asking about reason of convergence of series on Apostol Mathematical analysis ( Chapter - Lebesgue Integral)

2 votes
Accepted

martingale question for sums of N(0,1) random variables

2 votes

A corollary of Doob's inequality for general submartingales

2 votes

Multivariate normal with diagonal variance implies its components are normally distributed.

1 vote
Accepted

Proof of a corollary for the Strong Law of Large Number

1 vote

Doob-like equality with conditional expectation

1 vote
Accepted

What effect does the variance of a sequence of random variables $\{X_n\}$ have on their uniform integrability?

1 vote

Prove that $M_t=\left(\int_0^t f(s)dB_s\right)^2-\int_0^t f(s)^2ds$ is a martingale.

1 vote

A Conjecture on the Moment Generating Function of Functions of Sub-Gaussian Random Variables

1 vote

Convergence of expectation of inverse sum of random variables

1 vote

Why in some textbooks, the range of $\text{ArcCosh}(x)$ is given $[0, \infty)$?

1 vote
Accepted

The tangent line is the best "linear" approximation to the graph of a differentiable function

1 vote
Accepted

Prove that (orthogonal) projections $P_{L_1}x=P_{L_1}(P_{L_2}x)$ for closed subspaces $L_1\subset L_2\subset H $

1 vote

Geometric distributions converging to exponential distribution

1 vote

Linearity of Conditional Expectation

1 vote
Accepted

Prove $\{X_k\}_{k=1}^{n}$ are independent iff $F_{X_1,X_2,\ldots,X_n}(x_1,x_2,\ldots,x_n)=\prod_{k=1}^{n}F_{X_k}(x_k)$

0 votes

Why does convergence in distribution not imply convergence in mean square sense?