A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

Duality with time-changed Lévy processes

In this paper we study the pricing problem of derivatives written in terms of a two dimensional time{changed L¶evy processes. Then, we examine an existing relation between prices of put and call options, of both the European and the American type. This relation is called put{call duality. It includes as a particular case, the relation known as put{call symmetry. Necessary and su±cient conditions for put{call symmetry to hold are shown, in terms of the triplet of local charac- teristic of the Time{changed L¶evy process. In this way we extend the results obtained in Fajardo and Mordecki (2004) to the case of time{changed Lévy processes.

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31

Lévy processes and the Brazilian market

No presente artigo apresentamos processos de Levy usados na literatura para modelar os retornos dos ativos financeiros, estes processos sao gerados pelas distribuições Pareto-Estaveis e Hiperbolicas. Estudamos algumas propriedades destas distribui<;oes, em particular a propriedade da invariancia da escala temporal. Por ultimo apresentamos evidencias empiricas da aplicabilidade destes processos para modelar retornos de ativos Brasileiros, para isto usamos 0 Ibovespa, o recibo da Telebras e Petrobras, na amostra usamos dados dos periodos de 1 de janeiro de 1995 a 31 de dezembro de 1998 (Gl) e de 12 de janeiro de 1996 a 31 de dezembro de 1997(G2).

The gradually truncated Levy flight for systems with power-law distributions

Power-law distributions have been observed in various economical and physical systems. Levy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the gradually truncated Levy flight in which large steps of a Levy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Corrective experiences in psychotherapy: Definitions, processes, consequences, and research directions

After 5 years of conceptualizing, investigating, and writing about corrective experiences (CEs), we (the authors of this chapter) met to talk about what we learned. In this chapter, we summarize our joint understanding of (a) the definition of CEs; (b) the contexts in which CEs occur; (c) client, therapist, and external factors that facilitate CEs; (d) the consequences of CEs; and (e) ideas for future theoretical, clinical, empirical, and training directions. As will become evident, the authors of this chapter, who represent a range of theoretical orientations, reached consensus on some CE-related topics but encountered controversy and lively debate about other topics. (PsycINFO Database Record (c) 2013 APA, all rights reserved)

Quasi-Self-Dual Exponential Lévy Processes

The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Geochemistry Of Acid Mine Drainage From A Coal Mining Area And Processes Controlling Metal Attenuation In Stream Waters, Southern Brazil.

Acid drainage influence on the water and sediment quality was investigated in a coal mining area (southern Brazil). Mine drainage showed pH between 3.2 and 4.6 and elevated concentrations of sulfate, As and metals, of which, Fe, Mn and Zn exceeded the limits for the emission of effluents stated in the Brazilian legislation. Arsenic also exceeded the limit, but only slightly. Groundwater monitoring wells from active mines and tailings piles showed pH interval and chemical concentrations similar to those of mine drainage. However, the river and ground water samples of municipal public water supplies revealed a pH range from 7.2 to 7.5 and low chemical concentrations, although Cd concentration slightly exceeded the limit adopted by Brazilian legislation for groundwater. In general, surface waters showed large pH range (6 to 10.8), and changes caused by acid drainage in the chemical composition of these waters were not very significant. Locally, acid drainage seemed to have dissolved carbonate rocks present in the local stratigraphic sequence, attenuating the dispersion of metals and As. Stream sediments presented anomalies of these elements, which were strongly dependent on the proximity of tailings piles and abandoned mines. We found that precipitation processes in sediments and the dilution of dissolved phases were responsible for the attenuation of the concentrations of the metals and As in the acid drainage and river water mixing zone. In general, a larger influence of mining activities on the chemical composition of the surface waters and sediments was observed when enrichment factors in relation to regional background levels were used.

Construction Of A Manual Of Work Processes And Techniques From Centro De Dispensação De Medicamentos De Alto Custo (cedmac), Hospital De Clínicas, Unicamp.

The Centers for High Cost Medication (Centros de Medicação de Alto Custo, CEDMAC), Health Department, São Paulo were instituted by project in partnership with the Clinical Hospital of the Faculty of Medicine, USP, sponsored by the Foundation for Research Support of the State of São Paulo (Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP) aimed at the formation of a statewide network for comprehensive care of patients referred for use of immunobiological agents in rheumatological diseases. The CEDMAC of Hospital de Clínicas, Universidade Estadual de Campinas (HC-Unicamp), implemented by the Division of Rheumatology, Faculty of Medical Sciences, identified the need for standardization of the multidisciplinary team conducts, in face of the specificity of care conducts, verifying the importance of describing, in manual format, their operational and technical processes. The aim of this study is to present the methodology applied to the elaboration of the CEDMAC/HC-Unicamp Manual as an institutional tool, with the aim of offering the best assistance and administrative quality. In the methodology for preparing the manuals at HC-Unicamp since 2008, the premise was to obtain a document that is participatory, multidisciplinary, focused on work processes integrated with institutional rules, with objective and didactic descriptions, in a standardized format and with electronic dissemination. The CEDMAC/HC-Unicamp Manual was elaborated in 10 months, with involvement of the entire multidisciplinary team, with 19 chapters on work processes and techniques, in addition to those concerning the organizational structure and its annexes. Published in the electronic portal of HC Manuals in July 2012 as an e-Book (ISBN 978-85-63274-17-5), the manual has been a valuable instrument in guiding professionals in healthcare, teaching and research activities.

Agrin And Perlecan Mediate Tumorigenic Processes In Oral Squamous Cell Carcinoma.

Oral squamous cell carcinoma is the most common type of cancer in the oral cavity, representing more than 90% of all oral cancers. The characterization of altered molecules in oral cancer is essential to understand molecular mechanisms underlying tumor progression as well as to contribute to cancer biomarker and therapeutic target discovery. Proteoglycans are key molecular effectors of cell surface and pericellular microenvironments, performing multiple functions in cancer. Two of the major basement membrane proteoglycans, agrin and perlecan, were investigated in this study regarding their role in oral cancer. Using real time quantitative PCR (qRT-PCR), we showed that agrin and perlecan are highly expressed in oral squamous cell carcinoma. Interestingly, cell lines originated from distinct sites showed different expression of agrin and perlecan. Enzymatically targeting chondroitin sulfate modification by chondroitinase, oral squamous carcinoma cell line had a reduced ability to adhere to extracellular matrix proteins and increased sensibility to cisplatin. Additionally, knockdown of agrin and perlecan promoted a decrease on cell migration and adhesion, and on resistance of cells to cisplatin. Our study showed, for the first time, a negative regulation on oral cancer-associated events by either targeting chondroitin sulfate content or agrin and perlecan levels.