A GENERAL FORM OF THE INCREMENTS OF A TWO-PARAMETER WIENER PROCESS

In this paper,we consider a general form of the increments for a two-parameter Wiener process.Both the Csorgo-Revesz‘s increments and a class of the lag increments are the special cases of this general form of increments.Our results imply the theorem that have been given by Csorgo and Revesz(1978),and some of their conditions are removed.     

How big are the Csrg"非汉字符号"-Révész increments of two-parameter Wiener processes?

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.     

Infinitesimal nonrigidity of convex surfaces with planar boundary

In the present paper infinitesimal nonrigidity of a class of convex surfaces with planar boundary is given. This result shows that if the image of the Gauss map of an evolution convex surface with planar boundary covers some hemisphere, this surface may be of infinitesimal nonrigidity for the isometric deformation of planar boundary.     

Moderate deviations and functional limits for random processes with stationary and independent increments

We first give a functional moderate deviation principle for random processes with stationary and independent increments under the Ledoux's condition. Then we apply the result to the functional limits for increments of the processes and obtain some Csorgo-Revesz type functional laws of the iterated logarithm.     

Markov process functionals in finance and insurance

The Markov property of Markov process functionals which are frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Markov property of some important Markov process functionals are presented, the following conclusions are obtained： the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent increments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Markov process being still a Markov process are given.     

HOW BIG ARE THE LAG INCREMENTS OF A TWO PARAMETER WIENER PROCESS?~(**)

The author discusses how big the lag increments of a two-parameter Wiener processare and proves the same results as in[4].These results extende and improve the results ofthe increments of a two-parameter Wiener process in[1—3].     

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^N＋1

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in C^N＋1 near the origin, and the connected component containing the identity transformation of all locally holomorphic automorphisms of these hypersurfaces near the origin.     

闭排队网络中性能势与无穷小实现因子之间的关系

In this paper,the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non IPA approaches. Finally,another physical meaning of the service rate is given.     

MAURER-CARTAN EQUATION OF A∞-ALGEBRAS

The axioms of A∞-algebras can be written as Maurer-Cartan equation. Infinitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F-product.     

POLYNOMIALLY BOUNDED COSINE FUNCTIONS

We characterize polynomial growth of cosine functions in terms of the resolvent of its generator and give a necessary and sufficient condition for a cosine function with an infinitesimal generator which is polynomially bounded.     

Numerical solutions for asymmetric Lévy flights

Numerical Algorithms - Lévy flights are generalised random walk processes where the independent stationary increments are drawn from a long-tailed α-stable jump length distribution. We...     

Visco-elasticité et Processus de Lévy

We show that the linear visco-elastic materials, and more generally the physical phenomena to which Biot's relaxation theory is relevant, can be put in correspondance with the laws of processes with independent increments. In the one-dimensional case this correspondence is one to one with subordinators and gives rise naturally to a conjugation relation on subordinators.     

Une méthode de bandes et une méthode de cellules pour l'évaluation par défaut de la fréquence fondamentale d'une membrane

Summary For the first eigenvalue ₁ of a vibrating membrane, the «method of one-dimensional auxiliary problems» gave the lower bounds (19). We present here two new interpretations of those bounds, by means of cutting the membrane either into infinitesimal strips or else into infinitesimal quadratic cells, and adding positive or negative elastic support on each side of each cut.     

Quelques propriétés des opérateurs angle-bornés etn-cycliquement monotones

The paper deals with properties of σ-angle bounded linear and nonlinear operators. In particular it is proved that ifA is a σ-angle bounded linear maximal monotone operator in a real Hilbert space then ?A is the infinitesimal generator of an analytic semi-group.     

Representations of homogeneous quantum Lévy fields

We study homogeneous quantum Lévy processes and fields with independent additive increments over a noncommutative *-monoid. These are described by infinitely divisible generating state functionals, invariant with respect to an endomorphic injective action of a symmetry semigroup. A strongly covariant GNS representation for the conditionally positive logarithmic functionals of these states is constructed in the complex Minkowski space in terms of canonical quadruples and isometric representations on the underlying pre-Hilbert field space. This is of much use in constructing quantum stochastic representations of homogeneous quantum Lévy fields on Itô monoids, which is a natural algebraic way of defining dimension free, covariant quantum stochastic integration over a space-time indexing set.     

Convex ordering criteria for Lévy processes

Modelling financial and insurance time series with Lévy processes or with exponential Lévy processes is a relevant actual practice and an active area of research. It allows qualitatively and quantitatively good adaptation to the empirical statistical properties of asset returns. Due to model incompleteness it is a problem of considerable interest to determine the dependence of option prices in these models on the choice of pricing measures and to establish nontrivial price bounds. In this paper we review and extend ordering results of stochastic and convex type for this class of models. We also extend the ordering results to processes with independent increments (PII) and present several examples and applications as to α-stable processes, NIG-processes, GH-distributions, and others. Criteria are given for the Lévy measures which imply corresponding comparison results for European type options in (exponential) Lévy models.     

Lifting Lévy processes to hyperfinite random walks

An internal lifting for an arbitrary measurable Lévy process is constructed. This lifting reflects our intuitive notion of a process which is the infinitesimal sum of its infinitesimal increments, those in turn being independent from and closely related to each other - for short, the process can be regarded as some kind of random walk (where the step size generically will vary). The proof uses the existence of càdlàg modifications of Lévy processes and certain features of hyperfinite adapted probability spaces, commonly known as the “model theory of stochastic processes”.     

On the refracted–reflected spectrally negative Lévy processes

We study a combination of the refracted and reflected Lévy processes. Given a spectrally negative Lévy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a constant rate is subtracted from the increments of the process. Using the scale functions, we compute the resolvent measure, the Laplace transform of the occupation times as well as other fluctuation identities that will be useful in applied probability including insurance, queues, and inventory management.     

Some results on local growth of two-parameter Lévy processes

Summary In this article we consider some problems on local growth of 2-parameter Lévy processes, i.e., processes with independent and stationary increments, indexed by [0,+∞)×[0,+∞). The results are for the upper growth of these processes, at a fixed “time”z ₀.     

Un théorème de Torelli infinitésimal à coefficients

We generalize an infinitesimal Torelli theorem for hypersurfaces of high degree of M. Green (1985) [1], for twisted coefficients.