PARAMETRIC ESTIMATION OF DIFFUSION PROCESSES SAMPLED AT FIRST EXIT TIME

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross' model and the constant elasticity of variance (CEV) process illustrate the use of the technique proposed herein.Continuous time Markov processes, discrete time sampling, diffusions, interest rate models, stochastic algorithms.

State Tameness: A New Approach for Credit Constrains

We propose a new definition for tameness within the model of security prices as It\^o processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims and American contingent claims that we obtain does not require the full range of the volatility matrix. The technique used to prove the theorem on valuation of American contingent claims does not depend on the Doob-Meyer decomposition of super-martingales; its proof is constructive and suggest and alternative way to find approximations of stopping times that are close to optimal.arbitrage, pricing of contingent claims, continuous-time financial markets, tameness

Using a damper amplification factor to increase energy dissipation in structures

AbstractFluid dampers are an important tool for dissipating unwanted vibrations in a range of engineering structures. This paper examines the effects of amplifying the displacements transferred to a non-linear damper, to increase the effectiveness of the damper in a range of situations commonly encountered in civil engineering structures. These include, (i) the ability to “fine tune” the required damping for a particular size damper, (ii) the ability to have a set of the same size dampers, but with different amplification factors to achieve a specific damping task, and (iii) to increase the sensitivity of the damper to small movements which effectively extends the range over which the damper works. Through numerical simulations and experimental tests conducted on a non-linear damper, we quantify the potential advantages of adding an amplification factor and the range of parameters where the benefit to this device is significant. The example of a two-storey structure is used as a test case and real-time dynamic substructuring tests are used to assess the complete system performance using a range of different amplification factors. The results show that the structural performance is most improved for frequencies close to resonance and that the amplification factor has an effective limit that for the case considered in this study is of approximately 3. The effects of the mechanism compliance are also assessed

Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first-order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree-of-freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi-degree-of-freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures

An Approach of Randomness of a Sample Based on Its Weak Ergodic Limit

For a Polish Sample Space with a Borel σ-field with a surjective measurable transformation, we define an equivalence relation on sample points according to their ergodic limiting averages. We show that this equivalence relation partitions the subset of sample points on measurable invariant subsets, where each limiting distribution is the unique ergodic probability measure defined on each set. The results obtained suggest some natural objects for the model of a probabilistic time-invariant phenomenon are uniquely ergodic probability spaces. As a consequence of the results gained in this paper, we propose a notion of randomness that is weaker than recent approaches to Schnorr randomness

Comprensión de algunos conceptos geométricos en el contexto de la agricultura del café

La identificación de los bajos niveles de comprensión y de conceptualización de los estudiantes sobre elementos geométricos, fue la principal motivación y el punto de partida para el desarrollo de la presente investigación. En particular, se evidenció que los estudiantes no tienen clara la definición de los términos de área y perímetro y que, además, suelen asumir que las medidas de ambos son mutuamente dependientes. Al percibir que los contextos y ambientes lugareños tales como distribución de suelos para sembrados, la delimitación de propiedades o la uniformidad en algunos de los espacios agrícolas, favorecen la comprensión de los conceptos objeto de estudio aquí referenciados, se diseñó y evaluó una guía curricular bajo los parámetros y principios del marco teórico de la Enseñanza para la Comprensión4, que permitiera el avance y la caracterización de los procesos de comprensión en los estudiantes de la comunidad cafetera del corregimiento Santa Rita, municipio de Andes, departamento de Antioquia, Colombia