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o*******w
发帖数: 349 | 2 “Exponential inequalities for martingales and asymptotic properties of the
free energy of directed polymers in a random environment”
Quansheng Liu Frédérique Watbled
http://www.sciencedirect.com/science/article/pii/S0304414909000
这篇文章是关于概率领域 concentration inequalities in martingales. 以往的工作
都是假设bounded variables (X1, X2, …Xn) 。该文章讨论 unbounded Xi.
文章中关键的Lemma 2.3.的证明(page 3106) 说由 (2.6)（这是该引理的条件）：
E{exp(t*Xi) | F_(i-1)} < exp(Li(t))
归纳法可得到 (2.7) ：
E{exp(t*Sn) } < exp{SUM Li(t)} , where Sn =... 阅读全帖 |
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q********e
发帖数: 1255 | 3 来自主题: Mathematics版 - 求两篇文章 1.
Munoz Rivera, Jaime E.(BR-FRJ-IM); Perla Menzala, Gustavo(BR-FRJ-IM)
Uniform rates of decay for full von Kármán systems of
dynamic viscoelasticity with memory.
Asymptot. Anal. 27 (2001), no. 3-4, 335–357.
2.
Munoz Rivera, Jaime E.(BR-LCC-RD); Perla Menzala, Gustavo(BR-FRJ-IM)
Decay rates of solutions to a von Kármán system for viscoelastic plates
with memory.
Quart. Appl. Math. 57 (1999), no. 1, 181–200.
d**********[email protected]
thanks a lot! |
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q********e
发帖数: 1255 | 4 Murakami, Satoru(J-OKSC-AM)
Exponential asymptotic stability for scalar linear Volterra equations.
Differential Integral Equations 4 (1991), no. 3, 519–525.
d**********[email protected]
3x a lot! |
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L*******t
发帖数: 2385 | 5 再吃数学饭的同学面前偶总是很自卑。。
俺在做数值解法。Asymptotic expansion，FBSDE/PDE/PIDE的。。
所以你懂的。
大家都在灌水啊。我觉得挺好玩的。 |
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L*m
发帖数: 235 | 6 统计了近十余年来中国大陆高校在四大刊物上的发文，有些是挂名的，但不管如何，还
是都统计了。全名单如下
Annals of Mathematics
A proof of Demailly’s strong openness conjecture
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
A solution of an L2 extension problem with an optimal estimate and
applications
Qi'an Guan（关启安 北京大学） Xiangyu Zhou（周向宇 中科院）
Construction of Cauchy data of vacuum Einstein field equations evolving to
black holes
Junbin Li（黎俊彬 中山大学） Pin Yu（于品 清华大学）
Special test configuration and K-stability of Fano varieties
Chi Li(李驰 普林斯顿大学 现stony broo... 阅读全帖 |
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L*******t
发帖数: 2385 | 7 这个和我说的还不太一样。
expansion asymptotics解quasi linear PDE和FBSDE的问题已经被我完全解决了。
我有统一的方法解任何一个quasi linear PDE，系数可以非连续和无界
很快就会submit和放到ssrn，arxiv上去：）
Advanced |
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o*******w
发帖数: 349 | 8 你如果再给详细点的信息，或许讨论会深入。因为我不是这个领域的。还得看文献。我
好像理解一点你的问题。
m 是质量，对吧？ 那么既然annihilated 的rate跟质量无关，能不能在问题描述的时
候先不提质量。那么你的问题就是，求粒子运动所涉及的参数，使asymptotic 的结果
是这些粒子全部消失？ |
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x********i
发帖数: 905 | 9 http://iccm.mcm.ac.cn/dct/page/1
Plenary Lectures
Group 1
Wei Zhang: RTF and L-functions
Kai-Wen Lan: Cohomology of automorphic bundles
Xinyi Yuan: On Faltings heights of CM abelian varieties
Jing Yu: On Linear Independence of Logarithms
Xuhua He: Cocenter of Hecke algebras
Jiu-Kang Yu: A GAGA theorem for p-adic groups
Jianya Liu: Manin's conjecture for a class of singular cubic
hypersurfaces
Lei Fu: Rigidity of $ell$-adic Sheaves
Si Li: Open-closed topologica... 阅读全帖 |
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j****x
发帖数: 943 | 10 turbulence, compressible flows (transonic, shockwave), multiphase
flows, combustion, Stochastic mechanics, molecular dynamics, complex
fluids, hydrodynamic instability
variational calculus, asymptotic analysis, topology, spectral methods,
density function theory, monte carlo .... |
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R******y
发帖数: 651 | 11 写的很好，很practical。
我只需要加一点，即便你所说的重整化的结果核试验不相符，也还有另一种解释。那就
是 renormalization process is based on asymptotic expansion. |
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c****e
发帖数: 2097 | 12 not familiar with any numerical methods, but generally speaking, you have to
know the asymptotic behavior of your integrand to decide what to do with
your -\infty.
if it dies away over there, for example, i guess you can take some large
negative value.
however, if the case is not so, then you should manipulate your integrand
and integration domain a bit doing some mapping so as not to lose the
important stuff.
实函数，而是比较复杂的含时算符（矩阵）的函数， 不能直接积分得到解析表达式，
而且积分表达式随着里头算符的具体表达式不同而不同。
数来代替负无穷？ |
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c****e
发帖数: 2097 | 13 3+1 is fine, like SW or N=4. the hole is not to consider fundamental quarks
or asymptotically free theories, so far. |
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x**h
发帖数: 173 | 14 A post-doctoral research associate position is immediately available in the
Nonlinear Dynamics Laboratory http://web.utk.edu/~xzhao9/ at the University of Tennessee, Knoxville. Research in the lab focuses on rhythmic dynamics and various nonlinear phenomena in biology and engineering systems.
Candidates with background in biophysics, computational biology, nonlinear
dynamics, or control systems, are encouraged to apply. Previous experience
on asymptotic analysis or bifurcation analysis will be |
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R******y
发帖数: 651 | 15 are you sure? Even for non-zero b, it is not difficult to find the
asymptotic form. |
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w****1
发帖数: 4931 | 16 It may look like dirt but it's really gold. If you were Steve Shenker and
thought hard enough about the analogous divergence of the asymptotic series
in string perturbation theory, you would have discovered D-branes years
before Polchinski did. |
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D***a
发帖数: 939 | 17 最近在折腾 Asymptote 画图软件，很不错。是在 metapost 的基础上搞得，有类 c++
的语法，和 letax 兼容，易于扩展，.... |
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c****e
发帖数: 2097 | 18
no one ever said it didn't exist, i didn't at least.
but it's not a physical state. asymptotic states one uses to define say S-
matrix, are just these states, and they don't satisfy usual integrable
criterions for hilbert spaces. (that was what i was getting at, at least.
and formally they belong to a 'rigged' hilbert space).
it's not a physical state unless it's in a free theory.
plane waves are only delta function integrable. |
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e**********n
发帖数: 359 | 19 It is hard to draw any conclusion from estimating Tc for a finite 2D system.
First of all, how do you pin down Tc from the finite and smooth observables
? Whatever your choice is, it is rather arbitrary. I bet your boss is not
familiar with literature on this subject. The 'correct' approach is finite
size scaling analysis. In your model, the scaling formulas are predicted by
2D non-linear sigma model. If you look at the total magnetization, it will
asymptotically take the form
M(T,L) = f(T/Le^{c... 阅读全帖 |
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s****a
发帖数: 238 | 20 asymptote语言，虽然上手难了点，但是更加灵活，值得花点时间去学
其实和latex难度差不多了，不是很复杂的图，拿着示例程序东拼西凑一个晚上就可以
画出来了，效果是专业级的，和latex的集成也很好 |
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r***w
发帖数: 35 | 21 I think the answer for (1) is 1 is p>q. Not familiar with distribution, but
from point of view of PDE, this is a bias random walk, the corresponding PDE
is covection-diffusion. The solution will approach to the drift term in
asymptotic sense. Then, phyiscally 1 is the solution. Mathematically, the
PDE is
u_t+(2p-1)u'=pu", where p>0.5. Then, upwind of conservation law is to right
always. So, hitting 5 always happen. |
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l******i
发帖数: 1404 | 22
or
get much more data, need sample size to be large enough.
不考虑时间的话，也就是你所有数据都是independent的话，不管是不是regression，
你所有的model和test都是基于asymptotic theory。如果你的sample size足够大，你
的model checking又足够多了的话,你的model应该一直是对的，不会有突然间model
break down的问题。
如果考虑时间correlation的话，你要不停变换model的predictors和volatility w.r.t
. time,最好用用ARMA(1,1), GARCH(1,1) 等等financial econometric的model试试，
还有很多其他更复杂的time series model可以让你的model里很多东西都跟时间有关,
接下来怎么做要看具体情况了。 |
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e*******d
发帖数: 740 | 23 1. Knowing call price and strike price, how to identify the density function
in risk neutral world.
2. Let us say that we play a game in which we generate a random walk, and
every time the walk is positive you pay me some amount, but as soon as the
walk becomes negative the first time, I am out and we no longer play. How
does the probability of me staying in the game behave asymptotically after
very many steps?
3. The IBM stock is trading today at 100 and pays no dividends. Let us now
assume fo |
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p*****k
发帖数: 318 | 24
redtulips, that's a very nice solution.
the asymptotic result for large n is c*x-(1-c)+O(1/x^n).
the coefficient c is:
int{from 0 to infty} dt exp{-2*int{from 0 to t} ds [1-exp(-s)]/s}
~0.747598, which is indeed very close to 3/4.
the earliest reference is
A.Renyi, "On a One-Dimensional Problem Concerning Random Place Filling" (1958) |
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r*****d
发帖数: 44 | 25 if p!=1/2, it should be 0 since non-typical sequences have vanishing
probabilty of occurance asymptotically. |
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t**g
发帖数: 1164 | 26 【 以下文字转载自 JobHunting 讨论区 】
发信人: ttgg (还在苦苦思索昵称中), 信区: JobHunting
标 题: 请教一个binary tree问题
发信站: BBS 未名空间站 (Fri Feb 26 00:18:36 2010, 美东)
一个unbalanced binary tree
每个节点记录一个整数
对每个节点值
左边的child小于当前节点
右边的child大于当前节点
所以你插入1,2,3,4,5...n,会得到一个depth=n的树
可是插入6,4,8,3,5,7,9，就会得到一个well balanced tree
问题：
What is the average asymptotic depth of a simple unbalanced search tree of
integers? Use O(n) notation and provide proof |
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p*****k
发帖数: 318 | 27 this is just a shot in the dark:
would guess the question is from some d&c algorithm - one is
more interested in the asymptotic behavior of T when n->infty.
(T is probably only defined on N->N, so n/6 could be floor[n/6], etc)
then one needs the general version of the master theorem:
http://en.wikipedia.org/wiki/Akra-Bazzi_method |
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z****g
发帖数: 1978 | 28 I can only come up with:
1. Do MLE
2. Just do normal LSE procedure, when sample size is large enough, the
estimator is asymptotic to MLE. |
|
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r**a
发帖数: 536 | 30 First of all, you thought FF three-factor model is an example of APT. I
disagree with you. Because the basic assumption of APT is the arbitrage free
, but in FF's original paper they did not use this assumption to derive
their model. Actually, in Cochrane's book "asset pricing" he mentioned
something like the FF model is in the category of CAPM but closer to APT.
Regarding to the difference of CAPM and APT, I'd like to say some technique
things. In CAPM the final formula won't contain any residu... 阅读全帖 |
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r**a
发帖数: 536 | 31 heat kernel on poincare plane and asymptotic expansion |
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r**a
发帖数: 536 | 32 I do not understand his formula either. He offered a 2nd order ODE with a BC
. But the solution of his ode will be a function instead of a number.
If you follow my idea, you can got S(n) ~ 0.5n+1.5W(n). Then use the
expectation martingale to get the prob. But as i mentioned, using a BM with
drift only can give you the asymptotic solution, which implies that if a and
b are big enough, then it should be a good estimation.
new |
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L*******t
发帖数: 2385 | 33 就是说你做过local stochastic vol的东西？我现在很喜欢asymptotic expansion的解
，校准起来方便…impl vol option price transition density都能用，你如果用这个
，就不用解方程了大概？？ |
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L*******t
发帖数: 2385 | 34 其实root finding也是有error的，如果你的expansion terms取多一些，误差也很小。
asymptotic expansion是收敛的。。
取决于你啦，我就是提出一种解决的办法，因为你说Heston Impl Vol的方程Invert起
来很困难，所以我就想到了这个。 |
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d********t
发帖数: 9628 | 35 尼玛你们paper一个model几十个参数，业界临时哪里找数据去fit？model的普及度随
variable数量指数衰减。 |
|
L*******t
发帖数: 2385 | 36 10几个参数的model我认为是一种failure啊，喉哥，你看过Rene Carmona的paper没啊
，Tangent Levy model，最多4-6个参数，别人能perfect fit你的initial Impl Vol
Surface |
|
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L*******t
发帖数: 2385 | 38 我搞了一个多月。。
是实话，是我“被”搞了一个多月。。。 |
|
r**a
发帖数: 536 | 39
time
You missed the point. If Hagan or Labordere's method is only small time
expansion, how can you imagine the formulas can be applied to 30Y swaption?
You should read paper and books more carefully and think more deeply. Hagan'
s method is operator perturbation. But you need to find what operator he is
perturbing and why the perturbation works.
The heat kernel expansion heavily depends on what heat equation you are
talking about. Based on your words, I may naively guess that you are talking
a... 阅读全帖 |
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g****r
发帖数: 4 | 40 我觉得你和楼主讨论的不是同个东西（虽然有联系）。你说的是regression 和make
love里面的model用什么basis，你可以采取regularization 减小某个basis 上的参数
。 楼主说的是PDE的expansion 方法，例如asymptotic expansion 和 WKB expansion.
不过我猜两者应该是有联系的，例如galerkin。我也是刚刚接触 |
|
L*******t
发帖数: 2385 | 41 我咋感觉MLE对付的是IID的分布，QMLE就灵活的多，asymptotically，QMLE->MLE |
|
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r**a
发帖数: 536 | 43 物理里面所有expansion 都是asymptotic 都不收敛。 |
|
f***l
发帖数: 73 | 44 这个得看入行多久吧？
你这个是 asymptotic 的标准吗？ |
|
B***y
发帖数: 83 | 45
Notice that it is a second order iteration equation, thus first write it as a
vector equation:
Y_(n+1) = A(n) * Y_(n) ,
where Y_n = (a(2n-1), a(2n))^t, where "t" means "transpose".
Easy to check that A(n) asymptotically behaves like (b 0
0 b )
Thus if |b| > 1, then the series Y_n will diverge, if |b|< 1 then the series
will converge. |
|
o*******e
发帖数: 31 | 46
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
so y=c1Exp[(A^0.5)x]+c2Exp[-(A^0.5)x]
then the first term will blow up when x-->oo, so the asymptotic
solution when x-->0 should be y=c2Exp[-(A^0.5)x].
I plan to set the sloution of original diff. eq has the form
y=v(x)Exp[-(A^0.5)], then make derivative of y respect to x. After
make the substitution of y'', y' & y, the original diff. eq becomes
v''+(1/x-2A^0.5)v'-(A^0.5)(1/x)v=0.
I think we can use the series solution method to get the solution
of v |
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f*******d
发帖数: 339 | 47 Thanks, now I see what is AdS. However, there are two points I
don't understand:
1. Why is another negative signature (time-like) dimension
introduced in string theory? Is there any motivation for this?
2. You said it is impossible to understand QCD at high energies
from traditional (perturbative) point of view. Is that an
typo? I though QCD has asymptotic freedom, so it should be easy
to understand at high energy. It is the low energy limit that
is difficult to understand perturbatively. |
|
f*******d
发帖数: 339 | 48 Not sure what do you mean. There is no negative curvature
around massive
particles on a rubber sheet, the curvature there is also
positive, and
away from the massive particle it is asymptotically flat.
I live in Columbus. |
|
l**n
发帖数: 67 | 49
I've already said and agree that the curvature near the
contacting point between the big massive body and the rubber
sheet is positive. This is because it is locally part of
a sphere if we assume the big massive body is a sphere.
We all agree at this point.
I also agree it is asymptotically flat far away from the
massive body but the question arises here that i will argue
the curvature goes to zero from some negative value not
positive value.
A easily thought of model of the rubber sheet will b |
|
l**i
发帖数: 5 | 50 n!=(2*pi*n)^(1/2)*(n/e)^n*f(n)
where f(n) is an asymptotic series with
the leading coefficient 1,
f(n)=1+1/(12*n)+1/(288*n*n)+... |
|
