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14h
comment Monotone property of transition density of rotational $\alpha$-stable process
Didn't know the relation between subordinator and rotational stable process before. Thank you very much!
14h
accepted Monotone property of transition density of rotational $\alpha$-stable process
19h
comment Monotone property of transition density of rotational $\alpha$-stable process
@saz Yes, I know subordination. But how to get the conclusion?
1d
revised Monotone property of transition density of rotational $\alpha$-stable process
edited tags
1d
asked Monotone property of transition density of rotational $\alpha$-stable process
2d
comment Uniformly Continuous Like Property of the Integration on Measure Space
Nice solution. Thank you very much!
Mar
24
comment How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
Get it. Thanks a lot!
Mar
23
comment How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
I think I thought wrong with the calculation of $c$. Could you give me some hint or reference of calculation of it? Thanks!
Mar
23
accepted How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
Mar
23
comment How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
Very nice! Honestly, the constant $c$ is exactly what I need. But with your help, I think I can do it myself. (It will need analytic extension, I think).
Mar
23
comment How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
@saz Got it. Thanks! And how to integrate it?
Mar
23
revised How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
added 19 characters in body
Mar
23
comment How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
@saz Edited. I thought $\int (i(x,y)1_{|y|\leq 1})|y|^{-\alpha-n}dy$=0 by symmetric with $y$. What is wrong here? Thanks!
Mar
23
asked How to integrate $\int_{\mathbb R^n}\left(1-e^{i(x,y)}+i(x,y)1_{|y|\leq1}\right)|y|^{-\alpha-n}dy$?
Jan
24
asked Is the space of discrete probabilities measurable in the space of probabilities with weak topology?
Jan
24
answered In the space of probability distributions, is the set of discrete distributions dense?
Jan
23
asked Uniqueness of random measure
Dec
17
awarded  Inquisitive
Dec
16
asked Question about the bounded requirement of the simple function of definition of stochastic integration
Dec
9
comment Suppose $ \lim \left( a_{n}+a_{n+1} \right)=0 $. Show that $ \lim a_{n}=0 $ or $ 0 < \limsup a_{n} $.
If $\limsup a_n<0$, there will be a contradiction. If $\limsup a_n=0$, prove $\liminf a_n=0$ by contradiction.