d*e
发帖数: 843 | 1 a stochastic process I(t)~N(0,v(t)), i.e. normal distributed with mean 0 and
variance v(t). If $v(t)->0$ as t->infty, do we have I(t) goes to 0 a.s.? |
l*******l
发帖数: 248 | 2 it seems
and
【在 d*e 的大作中提到】
: a stochastic process I(t)~N(0,v(t)), i.e. normal distributed with mean 0 and
: variance v(t). If $v(t)->0$ as t->infty, do we have I(t) goes to 0 a.s.?
|
Q***5
发帖数: 994 | 3 I(t) got to 0 in L_2 norm, but not necessarily a.s.
and
【在 d*e 的大作中提到】
: a stochastic process I(t)~N(0,v(t)), i.e. normal distributed with mean 0 and
: variance v(t). If $v(t)->0$ as t->infty, do we have I(t) goes to 0 a.s.?
|
d*e
发帖数: 843 | 4 http://mitbbs.com/article1/Quant/31266241_3_0.html
联想到一个老问题，我不知道chimbo的思路是不是这个意思，i.e.
I don't know how variance->0 would imply a.s. convergence to 0
【在 Q***5 的大作中提到】
: I(t) got to 0 in L_2 norm, but not necessarily a.s.
:
: and
|
a********e
发帖数: 508 | 5 a.s. => L2 converge => converge in probability
not the other way around
【在 d*e 的大作中提到】
: http://mitbbs.com/article1/Quant/31266241_3_0.html
: 联想到一个老问题，我不知道chimbo的思路是不是这个意思，i.e.
: I don't know how variance->0 would imply a.s. convergence to 0
|
d*e
发帖数: 843 | 6 ............
【在 a********e 的大作中提到】
: a.s. => L2 converge => converge in probability
: not the other way around
|
d*e
发帖数: 843 | 7 a.s. convergence doesn't imply L_2 either.
【在 a********e 的大作中提到】
: a.s. => L2 converge => converge in probability
: not the other way around
|
M****i
发帖数: 58 | 8 This is not ture because a classical result says:
Let (X_n)_n be a sequence of i.i.d normal random variables with law N(0,1),
then limsup_n (2logn)^(-1/2)X_n=1 a.s. |
a********e
发帖数: 508 | 9 right. I forgot the uniformly boundness condition on that part.but
a.s. can't be implied from other convergence in general
【在 d*e 的大作中提到】
: a.s. convergence doesn't imply L_2 either.
|
