bluuebunny/crossref_metadata_2025 huggingface dataset:
Fractal Geometric Modeling in Computer Graphics
Authors: Zair C. E. , Tosan E.
Published: October 2003

Free form techniques and fractals are complementary tools for modeling respectively man-made objects and complex irregular shapes. Fractal techniques, having the advantage of describing self-similar objects, suffer from the drawback of a lack of control of the fractal figures. In contrast, free form techniques provide a high flexibility with smooth figures. Our work focuses on the definition of an IFS-based model designed to inherit the advantages of fractals and free form techniques (control by a set of control points, convex hull) in order to manipulate fractal figures in the way as classical free form shapes (BÉZIER, spline). The work is essentially based on the study of the functional equation Φ(τ * t) = T Φ (t), where Φ is a continuous function, τ and T are both contractive affine operators. We prove that there is a strong relationship between this functional equation and IFS attractors. This relationship will be used for the construction of parametric fractal attractors.
Surface-Enhanced Optical Nonlinearities of Nanostructured Fractal Materials
Authors: Shalaev V. M. , Poliakov E. Y. , Markel V. A. , Safonov V. P. , Sarychev A. K.
Published: October 2003

Localization of optical excitations in fractal metal nanocomposites, such as colloidal aggregates, self-affine and semicontinuous films, results in strong enhancements of optical nonlinearities. The localized modes of fractals cover a broad spectral range, from the visible to the far-infrared. Results of both theoretical and experimental studies of enhanced nonlinear optical responses of fractal nanostructures are considered.
Fractal Character of Humin and its Components
Authors: Malekani Kalumbu , Rice James A. , Lin Jar-Shyong
Published: October 2003

Natural organic matter in soils is usually found in intimate association with inorganic materials, primarily aluminosilicates, during the early stages of diagenesis to form an organo-mineral composite known as humin. Such composites typically represent more than 50% of the organic carbon present. Because of humin's insolubility and the surface reactivity of its organic components it is recognized as an important adsorbent of many anthropogenic organic compounds introduced into natural soil systems. Fractal analysis of small-angle X-ray scattering data was used to characterize the surface roughness of four humin samples following sequential removal of organic matter. The surface fractal dimensions were observed to decrease with removal of organic matter which also resulted in a decrease in surface pore size. These results suggest that the mineral components of humin have smooth surfaces over length scales of ~ 1 to ~ 15 nm, and that it is the organic matter coatings that are responsible for their surface roughness. Models clay-organic compounds exhibited results that are consistent with the observation made for natural samples. The surfaces of all the components of humin were found to be dominated by micro- and mesopores that could explain humin's high sorptive uptake of organic chemicals in the environment.
Superconducting Fractal Multilayers
Authors: Sidorenko A. S.
Published: October 2003

The influence of fractal geometry on superconductivity has been studied for layered superconductors. Superconducting multilayers consisting of alternating Nb and Cu layers with fractal stacking sequence and fractal dimension Df=0.63 including the two limiting cases Df= 0 (single superconducting film) and Df=1 (periodic multilayers) were prepared by electron-beam evaporation in ultrahigh vacuum. The layers of Nb and Cu were put down alternately via computer control of the target shutter. The structure of the samples has been checked with in situ reflection high-energy electron diffraction (RHEED) and Auger depth profiling, confirmed the prescribed layering geometry. Superconductivity was investigated by measurements of the critical temperature of superconducting transition Tc, and of the temperature and of the angular dependence of the upper critical magnetic fields Bc2. The observed dependences of Tc on the parameters of fractal samples are in a good qualitative agreement with the proximity effect theory developed for layered superconductors with a self-similar fractal structure. The behavior of the upper critical magnetic field is directly related to the type of the layering. At low temperatures, all samples show the same two-dimensional behavior essentially governed by the topological dimension of the individual superconducting layers, independent of the fractal dimensionality Df of the samples, whereas for temperatures near Tc the type of layering determines the dimensionality, resulting in a multicrossover behavior of fractal samples. The angular dependence of the upper critical magnetic field Bc2(θ) of fractals corresponds to the theory for a two-dimensional superconductor at all temperatures, reflecting the multicrossover behavior of the fractal multilayers, as long as the temperature-dependent coherence length is comparable with a certain scale of fractal.
Fractal Patterns of Tracers Advected by Smooth Temporally Irregular Fluid Flows and their Analysis by Use of Random Maps
Authors: Ott E. , Antonsen T. M. , Jacobs J.
Published: October 2003

Temporally irregular, large spatial scale, fluid advection of passive tracers occurs in a wide variety of situations. Our main point is that these situations can be conveniently conceptualized as resulting from successive application of a sequence of random maps. This viewpoint is numerically convenient and also provides a useful theoretical framework for dynamical-systems-based analyses of the resulting fractal patterns. Examples of three different situations are discussed: (i) the fractal distribution of passive scalar gradients, (ii) the fractal pattern formed by a scum floating on the surface of a moving fluid, and (iii) the pattern of particles entrained as they flow past an obstacle in an open flow.
Interactions: Solar and Laser Beams in Stratus Clouds, Fractals & Multifractals in Climate & Remote-Sensing Studies
Authors: Davis Anthony B. , Marshak Alexander , Cahalan Robert F. , Wiscombe Warren J.
Published: October 2003

Recent research on cloud structure and cloud-radiation interaction at NASA's Goddard Space Flight Center is presented as a show case of interdisciplinary work where fractals and multifractals play a central role. Focus has been primarily on stratocumulus because of their first-order effect on the Earth's energy balance (hence the global climate) due to their unusual horizontal extension and persistence. These cloud layers have quasi-flat upper/lower boundaries and appear to be quite uniform but are highly variable inside. The general strategy has been: utilization of spatial statistics of in situ and remotely sensed data pertaining to cloud structure to constrain stochastic cloud models used in turn for radiative transfer simulations where artificial radiation fields are generated; these fields are compared to actual measurements. and so on, until a degree of closure is achieved. The major trends have been: i) computation and understanding of cloudradiative properties from the large scales of interest to Global Climate Models (over 102 km) down to the smallest observable scales (less than 10 m); ii) from predicting the outcome of "ideal" measurements to those of "real" ones with limited accuracy, sampling and averaging; iii) from passive to active remote-sensing methods; and iv) shifting from standard to wavelet-based analysis/modeling techniques. In terms of potential for impact on geophysical research at large, the most important contributions are: a) criteria for and measures of nonstationarity and intermittency in scale-invariant data; b) so-called "bounded" multifractal cascade models having a continuously variable degree of nonstationarity: c) a parameterization of the bulk effect of fractal variability on large-scale planetary albedo; and d) the basic scaling theory of radiative "smoothing" that explains non-trivially related multiple scattering phenomena in both solar- and lidar-based remote sensing. The last item also suggests new methods of observing clouds and new ways of processing cloud radiance data to retrieve physical cloud properties.
Thermal Relaxation of Initially Fractal Grain Boundaries
Authors: Streitenberger P. , Förster D. , Veit P.
Published: October 2003

The concept of fractal geometry is used to describe serrated and rugged grain boundaries in the pure materials Zinc and Titanium after deformation and heat treatment. The fractal dimension of the grain boundaries are determined by application of optical and scanning electron microscopy over a wide range of magnifications. Measurements of the coarsening kinetics of the initially fractal-like grain boundaries during isochronous as well as isothermal annealing are presented. The results of the annealing experiments can be explained by an analytic fractal coarsening model yielding the observed dependency of the time law of grain boundary smoothing on the initially fractal dimension of the grain boundaries. The results are supported by a Monte Carlo simulation of the smoothing process of single initially fractal grains.
When Should We be Prepared to Improve a Portfolio by Lacklustre Stocks? — A Note on Log-Optimal Portfolio Selection
Authors: Schäfer D.
Published: October 2003

As far as log-optimal portfolio selection is concerned the expected log-return of a portfolio may sometimes be improved by investing in stocks with smaller rather than greater expected log-return. Starting from explicit examples, a sufficient and necessary condition for this to happen in markets with log-normal return distributions is derived and discussed. Further implications to dimension reduction in portfolio selection are outlined.
High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation
Authors: Düring Bertram , Fournié Michel , Jüngel Ansgar
Published: October 2003

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
Pricing Risky Options Simply
Authors: Aurell Erik , Simdyankin Sergei I.
Published: October 2003

This paper is a follow-up of (Aurell and Życzkowski, 1996) [2] and (Aurell et al. 1996) [1]. We show that the prescription of pricing option by minimizing risk can be solved in a way that is quite similar to the Black–Scholes' approach. For a given discrete-time price process we determine an auxillary process, generally a pseudo-probability taking both negative and positive values, such that the price of the option in our prescription is the expected value upon maturation with respect to the auxillary process. We present a conjecture due to G. Wolczyńska that this auxillary process is in fact a (pseudo)-Markov process which admits a very simple description. Numerical results are presented in favor of the conjecture.
Taming Large Events: Optimal Portfolio Theory for Strongly Fluctuating Assets
Authors: Bouchaud J. P. , Sornette D. , Walter C. , Aguilar J. P.
Published: October 2003

We propose a method of optimization of asset allocation in the case where the stock price variations are supposed to have "fat" tails represented by power laws. Generalizing over previous works using stable Lévy distributions, we distinguish three distinct components of risk described by three different parts of the distributions of price variations: unexpected gains (to be kept), harmless noise inherent to financial activity, and unpleasant losses, which is the only component one would like to minimize. The independent treatment of the tails of distributions for positive and negative variations and the generalization to large events of the notion of covariance of two random variables provide explicit formulae for the optimal portfolio. The use of the probability of loss (or equivalently the Value-at-Risk), as the key quantity to study and minimize, provides a simple solution to the problem of optimization of asset allocations in the general case where the characteristic exponents are different for each asset.
Estimating Expected Exchange Rates Under Target Zone Regimes
Authors: Chen Zhaohui , Giovannini Alberto
Published: October 2003

This paper develops a simple econometric procedure for estimating expected exchange rate under target zones. We employ the linear projection methodology to make predictions without relying on any prior structural or distributional assumptions, and at the same time demonstrate that such a methodology has to be modified in an important way to account for the presence of the target zone band. The method is applied to test the credibility of exchange rate regimes and to estimate the unannounced band. Our empirical results show that the band effect is nontrivial for narrow target zones such as those in the Bretton Woods system.
Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility
Authors: Derman Emanuel , Kani Iraj
Published: October 2003

In this paper we present an arbitrage pricing framework for valuing and hedging contingent equity index claims in the presence of a stochastic term and strike structure of volatility. Our approach to stochastic volatility is similar to the Heath-Jarrow-Morton (HJM) approach to stochastic interest rates. Starting from an initial set of index options prices and their associated local volatility surface, we show how to construct a family of continuous time stochastic processes which define the arbitrage-free evolution of this local volatility surface through time. The no-arbitrage conditions are similar to, but more involved than, the HJM conditions for arbitrage-free stochastic movements of the interest rate curve. They guarantee that even under a general stochastic volatility evolution the initial options prices, or their equivalent Black–Scholes implied volatilities, remain fair.

We introduce stochastic implied trees as discrete implementations of our family of continuous time models. The nodes of a stochastic implied tree remain fixed as time passes. During each discrete time step the index moves randomly from its initial node to some node at the next time level, while the local transition probabilities between the nodes also vary. The change in transition probabilities corresponds to a general (multifactor) stochastic variation of the local volatility surface. Starting from any node, the future movements of the index and the local volatilities must be restricted so that the transition probabilities to all future nodes are simultaneously martingales. This guarantees that initial options prices remain fair. On the tree, these martingale conditions are effected through appropriate choices of the drift parameters for the transition probabilities at every future node, in such a way that the subsequent evolution of the index and of the local volatility surface do not lead to riskless arbitrage opportunities among different option and forward contracts or their underlying index.

You can use stochastic implied trees to value complex index options, or other derivative securities with payoffs that depend on index volatility, even when the volatility surface is both skewed and stochastic. The resulting security prices are consistent with the current market prices of all standard index options and forwards, and with the absence of future arbitrage opportunities in the framework. The calculated options values are independent of investor preferences and the market price of index or volatility risk. Stochastic implied trees can also be used to calculate hedge ratios for any contingent index security in terms of its underlying index and all standard options defined on that index.
The Pricing of Country Funds from Emerging Markets: Theory and Evidence
Authors: Errunza Vihang , Senbet Lemma W. , Hogan Ked
Published: October 2003

This paper provides a theoretical and empirical analysis of country funds focusing on emerging economies whose capital markets are not readily accessible to outside investors. We study country fund pricing and the associated policy implications under alternative variations of international market structure segmentation. We show that country funds traded in the developed capital markets can be beneficial in promoting the efficiency of pricing in the emerging capital markets and in enhancing capital mobilization by local firms. These efficiency gains vary depending upon the degree to which the emerging market securities are spanned by the core or advanced market securities, and cross-border arbitrage restrictions. A country fund premium or discount arises in our framework owing to access and substitution effects characterizing the relationship between the host and emerging markets. We present some empirical evidence supporting our principal predictions. In particular, we investigate the issues of country fund pricing, relative influences of the home market, the international market, the global closed-end fund factor, and the behavior of fund premia/discounts.
Internationally Diversified Investment Using an Integrated Portfolio Model
Authors: Konno Hiroshi , Li Jing
Published: October 2003

In this paper, we use a new integrated portfolio model which takes care of stocks and bonds of several countries to construct an internationally diversified portfolio. This serves as an alternative to the popular asset allocation strategy, in which the fund is first allocated to indices corresponding to diverse asset classes and then allocated to individual assets using appropriate models for each asset class. Our model, on the other hand, determines the allocation of the fund to individual assets in one stage by solving a large scale mean-variance or mean-absolute deviation model. Another important feature of this article is a newly developed strategy for hedging the exchange rate risk by using forward contracts on currencies.

Computational experiments using historical data collected in the capital market show that the new approach can serve as a more reliable and less expensive method for allocating the fund to diverse classes of assets.
The Mexican Crisis and the Behavior of Country-Fund Discounts: Renewing the Puzzle of Closed-End Fund Pricing
Authors: Kramer Charles , Smith R. Todd
Published: October 2003

Many studies have attempted to reconcile the behavior of closed-end fund prices with notions about the behavior of investors. Such studies have appealed to frictions (taxes, agency costs, and illiquidity) and investor sentiment to explain the puzzling behavior of fund prices. The events of December 1994 in Mexico, and subsequent effects on some funds' prices, have given rise to a new puzzle, extreme premia on closed-end funds that invest in Mexican stocks. We believe this new puzzle is not amenable to explanation by extant hypotheses. We offer a hypothesis of loss-aversion on the part of individual investors as a possible explanation, and outline the relevant effects that loss-aversion should have on fund discounts.
Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits
Authors: Wilmott Paul , Oztukel Asli
Published: October 2003

In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide "confidence limits" for the option value.
A New Model for Interest Rates
Authors: Epstein D. , Wilmott P.
Published: October 2003

There are many theories and models underlying the valuation of fixed income security portfolios. This work addresses the problem from a new perspective: the objective is to find a lower bound for the value of a portfolio of cash flows. We set up conditions for the evolution of a short-term interest rate and value a liability using its present value. We formulate a first-order nonlinear hyperbolic partial differential equation for the value, V, of the portfolio. We explore the solution of this equation and then hedge our portfolio with market-traded zero-coupon bonds of known value. We include some salient examples — generating the Yield Envelope and valuing caps, floors and bond options.
On Minimizing Risk in Incomplete Markets Option Pricing Models
Authors: Hammarlid Ola
Published: October 2003

I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance and risk from trading in options and stocks are presented. The problem of finding a risk minimizing strategy in an incomplete market model where a perfect hedge is not possible is analyzed. Using this strategy according to the approach of Bouchaud and Sornette the option is priced by a fair game condition. In this article I establish the equivalence between global and local risk minimization and prove an option price conjecture of Wolczyńska. I also investigate optimality for a stock portfolio with extra profit.
Information Transmission Across Eurodollar Futures Markets
Authors: Lim Kian-Guan , Terry Eric , How Desmond
Published: October 2003

Identical contracts traded at two distinct time zones but linked with a mutual offset system allow for round-the-clock trading. It is interesting to investigate the characteristics of information transmission in such a market. In this paper we employ GARCH specifications to model Eurodollar futures interest rate changes in IMM and in SIMEX. We employ the Causality-in-Variance test based on cross-correlation function to test hypotheses on the lead-lag relationships of volatilities between IMM and SIMEX. There is strong evidence of information transmission from IMM to SIMEX, and not vice-versa. However, during the 86 December till 88 September period, including contracts during the October 87 crash, there is evidence of causality also running from SIMEX to IMM.
Collapse of Detail
Authors: Pan Enlin
Published: October 2003

When bond prices can be described in a state-space framework, the no-arbitrage condition and the positivity of forward prices together impose such a tight restriction that only one functional form for the zero-coupon term structure is possible. The explicit form of the term structure is derived, without any parameters. Thus it is unnecessary and even counter-productive to try to specify the nature of interest rate dynamics. Bond pricing has exactly three degrees of freedom.
An Explicit Formula for Option Pricing in Discrete Incomplete Markets
Authors: Wolczyńska Grażyna
Published: October 2003

Some aspects of the pricing of European call option are disscussed. We consider the simplest case of an incomplete market in the situation when the model of the market is discrete and increments of shares prices have a multinomial distribution. We look for similarities between this model and the model of Cox, Ross and Rubinstein. In particular we consider the possibility of using induction backwards and we look for an optimal price and strategy using the method of risk-minimization step by step from the date of realization T to 0.
A Risk-Neutral Stochastic Volatility Model
Authors: Zhu Yingzi , Avellaneda Marco
Published: October 2003

We construct a risk-neutral stochastic volatility model using no-arbitrage pricing principles. We then study the behavior of the implied volatility of options that are deep in and out of the money according to this model. The motivation of this study is to show the difference in the asymptotic behavior of the distribution tails between the usual Black–Scholes log-normal distribution and the risk-neutral stochastic volatility distribution.

In the second part of the paper, we further explore this risk-neutral stochastic volatility model by a Monte-Carlo study on the implied volatility curve (implied volatility as a function of the option strikes) for near-the-money options. We study the behavior of this "smile" curve under different choices of parameter for the model, and determine how the shape and skewness of the "smile" curve is affected by the volatility of volatility ("V-vol") and the correlation between the underlying asset and its volatility.
Optimal Index Tracking Under Transaction Costs and Impulse Control
Authors: Buckley I. R. C. , Korn R.
Published: October 2003

We apply impulse control techniques to a cash management problem within a mean-variance framework. We consider the strategy of an investor who is trying to minimise both fixed and proportional transaction costs, whilst minimising the tracking error with respect to an index portfolio. The cash weight is constantly fluctuating due to the stochastic inflow and outflow of dividends and liabilities. We show the existence of an optimal strategy and compute it numerically.
Insider Trading in a Continuous Time Market Model
Authors: Grorud Axel , Pontier Monique
Published: October 2003

This paper uses the enlargement of Brownian filtrations and a probability change for modelling the observation of a financial market by an insider trader. A characterization of admissible strategies and a criterion for optimization are given. Then a statistical test is proposed to test whether or not the trader is an insider.
Deriving Closed-Form Solutions for Gaussian Pricing Models: A Systematic Time-Domain Approach
Authors: Levin Alexander
Published: October 2003

A systematic time-domain approach is presented to the derivation of closed-form solutions for interest-rate contingent assets. A financial system "asset — interest rate market" is assumed to follow an any-factor system of linear stochastic differential equations and some piece-wise defined algebraic equations for the payoffs. Closed-form solutions are expressed through the first two statistical moments of the state variables that are proven to satisfy a deterministic linear system of ordinary differential equations.

A number of examples are given to illustrate the method's effectiveness. With no restrictions on the number of factors, solutions are derived for randomly amortizing loans and deposits; any European-style swaptions, caps, and floors; conversion options; Asian-style options, etc. A two-factor arbitrage-free Gaussian term structure is introduced and analyzed.
Optimal Investment Strategy for Risky Assets
Authors: Maslov Sergei , Zhang Yi-Cheng
Published: October 2003

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.
An International Study of Efficiency and Risk in Money Markets
Authors: Miles David
Published: October 2003

There is a huge literature on whether forward rates of interest provide unbiased estimates of future interest rates. In most studies econometric evidence is presented which is apparently inconsistent with market efficiency; but more rarely is the economic, as opposed to statistical, significance of deviations from efficiency investigated. This paper uses accurate, up-to-date information on short term money market rates, from a common source, for all the major economies to assess efficiency and profit opportunities. The economic significance of deviations from the conditions required for efficiency are assessed by testing various trading rules.

The paper explores the potential to make profits from money market transactions based on simple rules derived from econometric analysis of the relation between current and future interest rates. We find that in many cases there are systematic divergences between forward rates and future spot interest rates for various currencies quoted on the London interbank market.
Dynamics of Spot, Forward, and Futures Libor Rates
Authors: Rutkowski Marek
Published: October 2003

Distributional properties of spot, forward, and futures Libor rates under martingale measures are studied in various arbitrage-free setups.
Minimum-Relative-Entropy Calibration of Asset-Pricing Models
Authors: Avellaneda Marco
Published: October 2003

We present an algorithm for calibrating asset-pricing models to the prices of benchmark securities. The algorithm computes the probability that minimizes the relative entropy with respect to a prior distribution and satisfies a finite number of moment constraints. These constraints arise from fitting the model to the prices of benchmark prices are studied in detail. We find that the sensitivities can be interpreted as regression coefficients of the payoffs of contingent claims on the set of payoffs of the benchmark instruments. We show that the algorithm has a unique solution which is stable, i.e. it depends smoothly on the input prices. The sensitivities of the values of contingent claims with respect to varriations in the benchmark instruments, in the risk-neutral measure. We also show that the minimum-relative-entropy algorithm is a special case of a general class of algorithms for calibrating models based on stochastic control and convex optimization. As an illustration, we use minimum-relative-entropy to construct a smooth curve of instantaneous forward rates from US LIBOR swap/FRA data and to study the corresponding sensitivities of fixed-income securities to variations in input prices.
A General Framework for Hedging and Speculating with Options
Authors: Korn Ralf , Wilmott Paul
Published: October 2003

In contrast to their role in theory, options are in practice not only traded for hedging purposes. Many investors also use them for speculation purposes. For these investors the Black–Scholes price serves only as an orientation, their decisions to buy, hold or hedge an option are also based on subjective beliefs and on their personal utility functions (in the widest possible sense). The aim of this paper is to present a general framework to include different types of investors, especially hedgers, pure speculators and speculators following strategies with bounded risk. We derive their subjective values of an option endogenously from the solution of their decision problems.
A Yang–Mills Inequality for Compact Surfaces
Authors: Sengupta Ambar
Published: October 2003

We consider the Yang–Mills action functional S YM on the infinite-dimensional space of connections on a bundle over a compact surface. We find a lower bound for S YM (ω) in terms of holonomies of the connection ω, the topology of the surface, and the topology of the bundle. An intermediate 'energy inequality' becomes an equality if and only if the connection is a critical point of the Yang–Mills action. Yang–Mills minima can also be understood using these inequalities.
Some New Examples of Lie Super-Algebra Representations Arising from Quantum Stochastic Calculus
Authors: Parthasarathy K. R.
Published: October 2003

Following the methods of Refs. 1 and 2 we construct here a family of Lie super-algebra representations in terms of quantum stochastic integrals.
A New Class of White Noise Generalized Functions
Authors: Cochran W. G. , Kuo H.-H. , Sengupta A.
Published: October 2003

The S-transform is studied as a mapping from a space of tensors to a space of functions over a complex space. The range of this transform is characterized in terms of analyticity and growth. These results are applied to a broad class of generalized functions in white noise analysis. These correspond to completions of the Gaussian L2-space which preserve orthogonality of Hermite polynomials. The S-transform is defined for the new generalized functions, and the range of this S-transform is identified in terms of analyticity and growth. Examples of the new spaces of generalized functions are given; these include distributions considered by Kondratiev and Streit, as well as new classes of distributions whose S-transforms have growth bounded by iterated exponentials.
Quantum White Noises and Free Fields
Authors: Huang Zhiyuan , Luo Shunlong
Published: October 2003

Nuclear Wick algebra of generalized operators generated by quantum white noise is introduced in order to formulate the formal manipulations in free fields at rigorous mathematical level. Solutions of second quantized field equations and various physical observables such as energy and momenta of the fields are realized as generalized operators adn the renormalizations through Wick ordering procedure are investigated from functional analytical point of view.
Contraction of Generalized Relative Entropy Under Stochastic Mappings on Matrices
Authors: Petz Dénes , Ruskai Mary Beth
Published: October 2003

The contraction coefficient of stochastic mappings between full matrix algebras is introduced with respect to a generalized relative entropy labeled by an operator convex function g. It is proved that the coefficient is actually independent of g, in particular, it can be most conveniently computed by means of the square function.
Analysis on Poisson and Gamma Spaces
Authors: Kondratiev Yuri G. , da Silva José L. , Streit Ludwig , Us Georgi F.
Published: October 2003

We study the spaces of Poisson, compound Poisson and Gamma noises as special cases of a general approach to non-Gaussian white noise calculus, see Ref. 18. We use a known unitary isomorphism between Poisson and compound Poisson spaces in order to transport analytic structures from Poisson space to compound Poisson space. Finally we study a Fock type structure of chaos decomposition on Gamma space.
Extension of the Dynamics of Unstable Systems
Authors: Antoniou I. , Suchanecki Z.
Published: October 2003

The work of the Brussels–Austin groups over the last six years has demonstrated that for unstable systems, classical or quantum, there exist spectral decompositions of the evolution In terms of resonances and resonance states which appear as eigenvalues and eigenprojections of the evolution operator. These new spectral decompositions are non-trivial only for unstable systems and define an extension of the evolution to suitable dual pairs. Duality here is the states/observables duality and the spectral decompositions extend the algebraic approach to dynamical systems to an intrinsically probabilistic and irreversible formulation. The extended formulation allows for probabilistic prediction and control beyond the traditional local techniques.
Knots and Matrix Models
Authors: Aref'eva I. Y. , Volovich I. V.
Published: October 2003

A generating function for knot diagrams is constructed. We consider a matrix model with d(N×N) matrices and show that in the limits N→∞ and d→0 the model describes the knot diagrams. The same limit in matrix string theory is also discussed. We speculate that a prototypical M(atrix) without matrix theory exists in void.
Quantum Stochastic Differential Equation is Unitarily Equivalent to a Symmetric Boundary Value Problem in Fock Space
Authors: Chebotarev Alexander M.
Published: October 2003

We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of the Schrödinger equations in Fock space: the strong resolvent limit is unitarily equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitarily equivalent to the symmetric (or Stratonovich) form of QSDE.

We also prove that QSDE is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps in phase and amplitude of components of Fock vectors belonging to the range of the resolvent. The corresponding Markov evolution equation (the Lindblad or Markov master equation) is derived from the boundary value problem for the Schrödinger equation.
Notions of Independence Related to the Free Group
Authors: Accardi Luigi , Hashimoto Yukihiro , Obata Nobuaki
Published: October 2003

The central limit problem for algebraic probability spaces associated with the Haagerup states on the free group with countably many generators leads to a new form of statistical independence in which the singleton condition is not satisfied. This circumstance allows us to obtain nonsymmetric distributions from the central limit theorems deduced from this notion of independence. In the particular case of the Haagerup states, the role of the Gaussian law is played by the Ullman distribution. The limit process is explicitly realized on the finite temperature Boltzmannian Fock space. The role of entangled ergodic theorems in the proof of the central limit theorems is discussed.
Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs
Authors: Hora Akihito
Published: October 2003

Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.
Interacting Fock Spaces Related to the Anderson Model
Authors: Lu Yun-Gang
Published: October 2003

A new type of interacting Boltzmannian Fock space, emerging from the stochastic limit of the Anderson model, is investigated. We describe the structure of the space and the form, assumed in this case, by the principles of factorization and of total connection. Using these principles, the vacuum expectation of any product of creation and annihilation operators can be calculated. By means of these results, for any test function, a system of diffrence equations satisfied by the moments of the field operator and an integral equation satisfied by their generating function is deduced. In many interesting cases this equation is solved and the vacuum distribution function of the field operator (even its density) is explicitly determined. This evidentiates a new phenomenon which cannot take place in the usual Fock spaces (and did not appear in the simplest examples of interacting Fock spaces): by taking different test functions, the vacuum distribution of the field operator does not change only parametrically, but radically. In particular we find the semi-circle, the reciprocal-semi-circle (or Arcsine), the double-beta,…, and many other distributions.
Functional Representations for Fock Superalgebras
Authors: Kupsch Joachim , Smolyanov Oleg G.
Published: October 2003

The Fock space of bosons and fermions and its underlying superalgebra are represented by algebras of functions on a superspace. We define Gaussian integration on infinite-dimensional superspaces, and construct super-analogs of the classical function spaces with a reproducing kernel — including the Bargmann–Fock representation — and of the Wiener–Segal representation. The latter representation requires the investigation of Wick ordering on Z2-graded algebras. As application we derive a Mehler formula for the Ornstein–Uhlenbeck semigroup on the Fock space.
Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
Authors: Gibilisco Paolo , Pistone Giovanni
Published: October 2003

The non-parametric version of Information Geometry has been developed in recent years. The first basic result was the construction of the manifold structure on ℳμ, the maximal statistical models associated to an arbitrary measure μ (see Ref. 48). Using this construction we first show in this paper that the pretangent and the tangent bundles on ℳμ are the natural domains for the mixture connection and for its dual, the exponential connection. Second we show how to define a generalized Amari embedding AΦ:ℳμ→SΦ from the Exponential Statistical Manifold (ESM) ℳμ to the unit sphere SΦ of an arbitrary Orlicz space LΦ. Finally we show that, in the non-parametric case, the α-connections ∇α(α∈(-1,1)) must be defined on a suitable α-bundle ℱα over ℳμ and that the bundle-connection pair (ℱα, ∇α) is simply (isomorphic to) the pull-back of the Amari embedding Aα: ℳμ→S2/1-α were the unit sphere S2/1-αcL2/1-α is equipped with the natural connection.
Free Coherent States and Distributions on p-Adic Numbers
Authors: Kozyrev S. V.
Published: October 2003

Free coherent states for a system with p degrees of freedom are defined. An isomorphism between the space free coherent states and the space of distributions on p-adic disk is constructed.
Unification of Independence in Quantum Probability
Authors: Lenczewski Romuald
Published: October 2003

Let [Formula: see text], be the conditionally free product of unital free *-algebras [Formula: see text], where ϕl, ψl are states on [Formula: see text], l∈I. We construct a sequence of noncommutative probability spaces [Formula: see text], m∈N, where [Formula: see text] and [Formula: see text], m∈N, [Formula: see text], and the states [Formula: see text], ϕl are Boolean extensions of ϕl, ψl, l∈I, respectively. We define unital *-homomorphisms [Formula: see text] such that [Formula: see text] converges pointwise to *l∈I(ϕl,ψl). Thus, the variables j(m)(w), where w is a word in [Formula: see text], converge in law to the conditionally free variables. The sequence of noncommutative probability spaces [Formula: see text], where [Formula: see text] and Φ(m) is the restriction of [Formula: see text] to [Formula: see text], is called a hierarchy of freeness. Since all finite joint correlations for known examples of independence can be obtained from tensor products of appropriate *-algebras, this approach can be viewed as a unification of independence. Finally, we show how to make the m-fold free product [Formula: see text] into a cocommutative *-bialgebra associated with m-freeness.
Weak Coupling Limit with a Removal of an Ultraviolet Cutoff for a Hamiltonian of Particles Interacting with a Massive Scalar Field
Authors: Hiroshima Fumio
Published: October 2003

A Hamiltonian of an interaction system between N-particles and a massive scalar field is considered. The Hamiltonian with an ultraviolet cutoff is defined as a self-adjoint operator acting in a Hilbert space. Renormalized Hamiltonians are defined by subtracting renormalization terms from the Hamiltonian. It is shown that N-body Schrödinger Hamiltonians can be derived from taking a weak coupling limit and removing the ultraviolet cutoff simultaneously for the renormalized Hamiltonians. In particular, in the case where the space dimension equals three, the Yukawa potential appears in the N-body Schrödinger Hamiltonian. It is also shown that, in the case where the space dimensions are one or two, infimum of the spectra of the renormalized Hamiltonians converge to those of the N-body Schrödinger Hamiltonians.
A C0-Group Generated by the Lévy Laplacian II
Authors: Saitô Kimiaki
Published: October 2003

In this paper we shall discuss a C0-group generated by the Lévy Laplacian and operators approximating that group in the strong topology of the space of generalized white noise functionals.
The Free Stochastic Limit of Interacting Quantum Fields
Authors: Gough John
Published: October 2003

The problem of obtaining the quantum stochastic limit for a system interacting with a reservoir is investigated when both are considered as quantum fields. The pre-limit fields are as encountered in standard quantum field theory and in particular we do not resort to the simplifying responseless interaction for the reservoir field. In the separation of time scales between the unperturbed (slow) and interaction (fast) dynamics we find a new quantum stochastic noise emerging which describes multi-particle scatterings and has extended free statistics. We give explicit diagrammatic rules to compute the 2n-point correlators of the noise.
Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus
Authors: Huang Zhiyuan , Luo Shunlong
Published: October 2003

A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated. As applications, quantum stochastic integrals and quantum stochastic differential equations are treated from the viewpoint of Wick calculus.
The Semi-Circle Diagrams in the Stochastic Limit of the Anderson Model
Authors: Accardi Luigi , Lu Yun Gang , Mastropietro Vieri
Published: October 2003

We prove that, in the stochastic limit of the Anderson model only the non-crossing diagrams survive for the transition amplitude from the first excited state of the free Hamiltonian to the first excited state of the interacting Hamiltonian. This confirms a conjecture of Migdal (1958) and Abrikosov, Gorkov, Dzyaloshinski (1975). From this we deduce a closed (nonlinear) Schwinger–Dyson type equation for the limit transition amplitude whose solution can be found and gives the explicit dependence of this amplitude on the momentum of the excited state.
On Some Markov Processes Arising from the Eyre-Hudson Super Lie Algebra Representations
Authors: Parthasarathy K. R.
Published: October 2003

It is well-known3,5 that Brownian motion and Poisson process arise naturally from the canonical commutation relations (CCR) of free field operators in a boson Fock space. Eyre and Hudson2 have recently shown how to construct fields of operators in a boson Fock space obeying super Lie commutation relations. We establish the essential self-adjointness of their real and imaginary parts on the domain ∊, the linear manifold generated by all the exponential (coherent) vectors and determine a family of Markov processes which they give rise to in a natural manner. These Markov processes yield examples of Evans–Hudson flows3,5 and Azéma-like martingales.1,4,6
Innovations for Random Fields
Authors: Hida Takeyuki , Si Si
Published: October 2003

There is a famous formula called Lévy's stochastic infinitesimal equation for a stochastic process X(t) expressed in the form [Formula: see text] We propose a generalization of this equation for a random field X(C) indexed by a contour C. Assume that the X(C) is homogeneous in a white noise x, say of degree n, we can then appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X(C) and hence its probabilistic structure. Some of future directions are also mentioned.
Time Evolution and Invariance of Boson Systems Given by Beam Splittings
Authors: Fichtner K.-H. , Liebscher V. , Freudenberg W.
Published: October 2003

Based on a model for general beam splittings we search for states of boson systems which are invariant under the combination of the evolution given by the splitting procedure and some inherent evolution. It turns out that for finite systems only trivial invariant normal states may appear. However, for locally normal states on a related quasilocal algebra representing states of infinite boson systems, one can find examples of nontrivial invariant states. We consider as example a beam splitting combined with a contraction compensating the loss of intensity caused by the splitting process. In general, we observe interesting connections between the splitting procedure and certain thinning operations in classical probability theory. Several applications to physics seem to be natural since these beam splitting models are used to describe measuring procedures on electromagentic fields.