跳扩散模型中亚式期权的定价

本文研究一类跳扩散模型中亚式期权的定价问题，得到了关于算术平均亚式期权的一个简单而统一的算法，并用偏微分方程的技巧将其定价问题归结为一个与路径依赖量无关的一维积分-微分方程的求解问题．     

Transport phenomena in a plane shock wave

With the use of the nonpolynomial closure 1/ _z in the Mott-Smith approximation of the solution of the Boltzmann equation, we obtain a value of the density gradient in the limit of a very weak shock wave that is close to the correct value. For the determination of the transverse temperature gradient we calculated the _x ² / _z moment of the Mott-Smith collision integral. The effective values of viscosity and thermal conductivity in the limit of a very weak shock wave were calculated for inverse-power potentials and found to agree almost exactly with the Chapman-Enskog values. Such a comparison can serve as a criterion for the evaluation of different bimodal theories. Various bimodal theories give different values of viscosity and thermal conductivity, but all of them give 33 % too high a value of the Eucken ratio.     

Some properties of an extended Wigner function

A covariant generalisation of Wigner function proposed by us some years ago is reviewed, and its remarkable and useful properties are elucidated; its being a natural solution to a relativistically covariant Liouville equation is also demonstrated.     

Joint availability of systems modelled by finite semi–markov processes

Consider a repairable system at the time instants t and t + x, where t, x ≥0. The joint availability of the system at these time instants is defined as the probability of the system being functional in both t and t + x. A set of integral equations is derived for the joint availability of a system modelled by a finite semi–Markov process. The result is applied to the semi–Markov model of a two–unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two–point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results obtained by this method are shown to be in good agreement with those from simulation.     

奇异积分方程理论在迁移方程中的应用

本文利用奇异积分方程理论，对于具有非零边界条件的球对称模型的散射裂为函数，给出了直接求妥方法并给出了解的明显表达式。     

Characterization of a Marshall-Olkin type class of distributions

Summary A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function. Work performed while the authors were members of CNR-GNAFA.     

On the kinetic theory of a dense gas of rough spheres

The revised Enskog equation for a dense gas of rough spheres is considered. TheH theorem and the conservation equations are discussed.     

Interface sharpness in the Ising model with long-range interaction

For the 3-dimensional Ising model with long-range interaction, Gibbs states are constructed that are small perturbations of non-translation-invariant ground states. These ground states are in one-to-one correspondence with the set of all rational planes.     

Front propagation in certain one-dimensional exclusion models

Recent results on two interacting particle systems on are summarized, the asymmetric simple exclusion process and the branching exclusion process.     

On the asymptotic equivalence between the Enskog and the Boltzmann equations

An asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the Boltzmann and Enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations. The proof is given starting from the solution of the Boltzmann equation, then the proof line is simply indicated when one starts from the Enskog equation. The proof holds for Knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the Enskog equation tends to zero.On leave from Department of Mathematics, University of Warsaw, Poland.