流形上随机流的渐近平坦性

本文的目的是讨论流形上由随机微分方程确定的扩散过程的体积零化性质。令X_t(x)是描述流形M上的微分同胚流x→X_t(x)的扩散过程,K是M中具有正有限Hausdorff测度的紧致曲面,我们给出X_t(K)的面积在t→∞时几乎必然趋于零的条件,特别地,随机流X_t(·)的渐近零化定向可求长弧r:[0,1]→M的弧长。     

Alternative Local Discriminant Bases Using Empirical Expectation and Variance Estimation

This article proposes alternative discriminant measures for selecting the best basis for classification purposes among a large collection of orthonormal bases organized in a binary tree structure. A generalization of the local discriminant basis algorithm of Saito and Coifman is constructed. The success of these new methods is evaluated and compared to earlier methods in experiments.     

Martingales Locales sur un Ouvert Droit Optionnel †

Dans les développements récents de la théorie des martingales locales, on a eu parfois besoin de localiser la notion de martingale locale à un intervalle stochastique du type [0, T[ (voir un commentaire dans Dellacherie-Meyer [l,p.444]). En corrigeant une erreur figurant dans un travail [4] de Kunita, Maisonneuve [5] a introduit une bonne notion de martingale locale continue sur un intervalle stochastique [0, T[. Cependant, si 1'on emprunte sa méthode pour définir les martingales locales non continues sur [0, T[, on arrivera, dans le cas o[ugrave] T=∞, non pas à la notion de martingale locale usuelle, mais à celle de martingale faible au sens de Kazamaki [3]. Nous nous proposons ici de définir, en modifiant légérement la méthode de Maisonneuve, les martingales locales sur [0, T[, ou plus généralement, sur un intervalle du type [S, T[, et d'étudier leurs propriétés. Aprés quoi, en nous inspirant d'un travail [8] tout récent de Zheng, nous introduisons une notion de martingale locale sur un ouvert droit optionnel, celle-ci étend une notion de martingale locale sur un ouvert prévisible, qui a été introduite par Zheng dans [8].     

稠密的s维分形集

对任意给定的0≤s≤1,本文构造Cantor型集E_s,使dim_H E_s=s,且E_s在[0,1]内稠密。     

Directed search process driven by Levy motion with stochastic resetting

In this paper, We show how certain active transport processes in living cellscan be modeled in terms of a directed search process driven by Levy motion with stochasticresetting. We consider the motor-driven intracellular transport of vesicles to synaptictargets in the axons and dendrites of neurons, in this case, the restart duration of thesearch process after reset is finite, which has two parts: a finite return time and a refractoryperiod. We use a probabilistic renewal method to calculate the splitting probabilities andconditional mean first passage times (MFPTs) for capture by a finite array of contiguoustargets. We consider two different search scenarios: bounded search on the interval [0, L],where L is the length of the array, with a refractory boundary at x = 0 and a reflectingboundary at x = L (Model A), and partially bounded search on the half-line (Model B).In the latter case there is a non-zero probability of can not to find a target in the absenceof resetting. We show that both models have the same splitting probabilities, and thatincreasing the resetting rate r will lead to the splitting probability increases. On theother hand the MFPTs for model A are monotonically increasing functions of r, whereasthe MFPTs of model B are non-monotonic respect to r, with a minimum at an optimalresetting rate.     

Conformal measures and Hausdorff dimension for infinitely renormalizable quadratic polynomials

We show in this paper that iff is a quadratic infinitely many times renormalizable polynomial of sufficient high combinatorial type, then: HD (J(f))= inf{: -conformal measure for f} We use Lyubich's construction of the principal nest ([Lyu97]) in order to prove this result.Partially supported by CNP q-Brazil grant # 300534/96-5     

The size of the Julia set of meromorphic functions

We give a lower bound of the hyperbolic and the Hausdorff dimension of the Julia set of meromorphic functions of finite order under very general conditions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

We analyze the local behavior of the Hausdorff centered measure for selfsimilar sets. If E is a self-similar set satisfying the open set condition, then Cs(E∩B(x,r)) ≤(2r)s for all x ∈ E and r 0, where Csdenotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.     

Hausdorff dimension of a random invariant set

The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension.     

区域信号配时模型的非平衡交通分配算法

本文研究了区域信号配时问题.采用遗传算法和非平衡交通分配的拟Frank-Wolfe算法来求解,通过实例对算法进行验证并与已有的算法结果进行了比较,结果表明算法是有效的,适合求解这类问题.     

Comparison of fractal measures

In this paper, the relationship between the s-dimensional Hausdorff measures and the g-measures in Rd is discussed, where g is a gauge function which is equivalent to ts and 0 < s≤d. It shows that if s=d, then Hg = c1Hd, Cg = c2Cd and Pg = c3Pd on Rd, where constants c1, c2 and c3 are determined by where Wg, Cg and Pg are the g-Hausdorff, g-central Hausdorff and g-packing measures on Rd respectively. In the case 0相似文献   

一类投资时点问题的最优停止模型及其等待时间

针对收益流与一次性投入沉淀成本均不确定的一类风险项目,为使其预期总的贴现净收益最大,提出了寻找项目最优投资时点的最优停止模型.这种方法不依赖于金融市场的完备性及市场无套利.借助于高切原理,通过求解一个自由边界问题,得到模型的候选解.运用最优停止理论证明了其的确为最优解,从而显式地给出了该类风险项目的最优投资时点.进一步,显式给出了到达最优时点的平均等待时间.     

Quitting games – An example

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r _S ⁱ, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon. Received: October 2001     

Analytic solution and estimation of parameters on a stochastic exponential model for a technological diffusion process

In this paper we examine the behaviour of a stochastic model that describes a technological diffusion process (continuously increasing process). Furthermore we obtain a solution for the proposed model through the estimation of the volatility using three different approximations. The adjustment of real data to the final stochastic model confirms its ability of describing and forecasting real cases.     

On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturitiesThis shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over timeIn this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issueTo make the problem clearly,we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes(1973), Briys and de Varenne(1997), i.e, the default barrier is KD(t, T) and the recovery rate is(1- ω), where D(t, T) is the price of zero coupon default free bond and ω is a constant(0 ω≤ 1)By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probabilityFurther, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt ≤ KD(t, T)and at the same time, the bondholder will receive(1- ω)Vt KBy introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probabilityNumerical results are presented to show the impact of different parameters to credit spread of bond.