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Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations
Stochastic delay dierential equation oscillation non-Coscillatio
2009/4/28
This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depen...
Poisson Statistics for the Largest Eigenvalues of Wigner Random Matrices with Heavy Tails
random matrices largest eigenvalues Poisson statistics
2009/4/28
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
山西省晋中地区外商投资企业调查报告
山西省 晋中地区 外商投资企业 调查报告
2009/4/14
山西省晋中地区外商投资企业的调查于1997年8月26日在全地区进行。根据晋中地区国税局所掌握的资料，对其有一定代表性的43家企业进行调查。得到了能反映本地区外商投资企业运营状况的具体资料。调查结果表明：改革开放以来，晋中地区外商投资企业不断扩大，特别是在93、94两年之间迅速增加，对我国的对外开放发挥了巨大的作用；根据山西的特点以及晋中地区的优势看，该地区外商投资在选煤，炼焦方面的几家企业规模较大...
一名统计学家遇到一位数学家，统计学家调侃数学家说道：“你们不是说若ｘ＝ｙ且ｙ＝ｚ，则ｘ＝ｚ吗！那么想必你若是喜欢一个女孩，那么那个女孩喜欢的男孩你也会喜欢喽！？”数学家想了一下反问道：“那么你把左手放到一锅一百度的开水中，右手放到一锅零度的冰水里想来也没事吧！因为它们平均的温度不过是五十度而已！”
Fixed Points of the Smoothing Transform：the Boundary Case
Fixed Points Smoothing Boundary Case
2009/4/8
Let $A=(A_1,A_2,A_3,ldots)$ be a random sequence of non-negative numbers that are ultimately zero with $E[sum A_i]=1$ and $E left[sum A_{i} log A_i right] leq 0$. The uniqueness of the non-negative fi...
On the Duality between Coalescing Brownian Particles and the Heat Equation Driven by Fisher-Wright Noise
Duality Brownian Particles Heat Equation Fisher-Wright Noise
2009/4/7
This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...
A Note on Occupation Times of Stationary Processes
Note Occupation Times Stationary Processes
2009/4/7
Consider a real valued stationary process $X={X_s:, sinRR}$. For a fixed $tin RR$ and a set $D$ in the state space of $X$, let $g_t$ and $d_t$ denote the starting and the ending time, respectively, of...
Poisson Thinning by Monotone Factors
Poisson Thinning Monotone Factors Poisson point processes
2009/4/7
Let X and Y be Poisson point processes on the real numbers with rates l_1 and l_2 respectively. We show that if l_1 > l_2, then there exists a deterministic map f such that f(X) and Y have the same di...
A Resummed Branching Process Representation for a Class of Nonlinear ODEs
representations Branching Process Nonlinear ODEs
2009/4/7
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
On the Chung-Diaconis-Graham random process
Chung Diaconis Graham considered random processes
2009/4/3
Chung, Diaconis, and Graham considered random processes of the form Xn+1=2Xn+bn (mod p) where X0=0, p is odd, and bn for n=0, 1, 2, ... are i.i.d. random variables on {-1,0,1}. If Pr(bn=-1)=Pr(bn=1)= ...
Some properties of exponential integrals of Levy processes and examples
properties exponential integrals Levy processes examples
2009/4/3
The improper stochastic integral $Z=int_0^{infty-}exp(-X_{s-})dY_s$ is studied, where ${ (X_t ,Y_t) , t ges 0 }$ is a L'evy process on $R ^{1+d}$ with ${X_t }$ and ${Y_t }$ being $R$-valued and $R ^d$...
We define and build H-fractional α-stable fields indexed by a metric space (E,d). We mainly apply these results to spheres, hyperbolic spaces and real trees
On the Existence of Recurrent Extensions of Self-similar Markov Processes
Self-similar Markov Processes self-similar recurrent extension
2009/4/2
Let X = (Xt)t ≥ 0 be a self-similar Markov process with values in the non-negative half-line, such that the state 0 is a trap. We present a necessary and sufficient condition for the existence of a se...
We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.
Integral criteria for transportation cost inequalities
criteria transportation cost inequality
2009/4/1
In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Ou...