Spectral analysis of diffusions with jump boundary

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.

On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Decay to equilibrium for jump processes with heavy tails

The case is made for a more careful analysis of the large time asymptotic of infinite particle systems in the thermodynamic limit beyond zero density. The insufficiency of current analysis even in the model case of free particles is demonstrated. Recent advances based on more sophisticated analytical tools like functions of mean variation and Hardy spaces are sketched.

Jump and variance risk premia in the S&P 500

We analyze the risk premia embedded in the S&P 500 spot index and option markets. We use a long time-series of spot prices and a large panel of option prices to jointly estimate the diffusive stock risk premium, the price jump risk premium, the diffusive variance risk premium and the variance jump risk premium. The risk premia are statistically and economically significant and move over time. Investigating the economic drivers of the risk premia, we are able to explain up to 63 % of these variations.

A systematic component of the jump-risk premium in an AJD model

We develop an affine jump diffusion (AJD) model with the jump-risk premium being determined by both idiosyncratic and systematic sources of risk. While we maintain the classical affine setting of the model, we add a finite set of new state variables that affect the paths of the primitive, under both the actual and the risk-neutral measure, by being related to the primitive's jump process. Those new variables are assumed to be commom to all the primitives. We present simulations to ensure that the model generates the volatility smile and compute the "discounted conditional characteristic function'' transform that permits the pricing of a wide range of derivatives.

A unified model for the long and high jump

A simple model based on, the maximum energy that an athlete can produce in a small time interval is used to describe the high and long jump. Conservation of angular momentum is used to explain why an athlete should, run horizontally to perform a vertical jump. Our results agree with world records. (c) 2005 American Association of Physics Teachers.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

The rating of perceived exertion predicts intermittent vertical jump demand and performance

The aims of this study were (a) to assess the ability of the rating of perceived exertion (RPE) to predict performance (i.e. number of vertical jumps performed to a fixed jump height) of an intermittent vertical jump exercise, and (b) to determine the ability of RPE to describe the physiological demand of such exercise. Eight healthy men performed intermittent vertical jumps with rest periods of 4, 5, and 6s until fatigue. Heart rate and RPE were recorded every five jumps throughout the sessions. The number of vertical jumps performed was also recorded. Random coefficient growth curve analysis identified relationships between the number of vertical jumps and both RPE and heart rate for which there were similar slopes. In addition, there were no differences between individual slopes and the mean slope for either RPE or heart rate. Moreover, RPE and number of jumps were highly correlated throughout all sessions (r=0.97-0.99; P0.001), as were RPE and heart rate (r=0.93-0.97; P0.001). The findings suggest that RPE can both predict the performance of intermittent vertical jump exercise and describe the physiological demands of such exercise.

Evaluation of an Innovative Critical Power Model in Intermittent Vertical Jump

The aim of this study was to test if the critical power model can be used to determine the critical rest interval (CRI) between vertical jumps. Ten males performed intermittent countermovement jumps on a force platform with different resting periods (4.1 +/- 0.3 s, 5.0 +/- 0.4 s, 5.9 +/- 0.6 s). Jump trials were interrupted when participants could no longer maintain 95% of their maximal jump height. After interruption, number of jumps, total exercise duration and total external work were computed. Time to exhaustion (s) and total external work (J) were used to solve the equation Work = a + b . time. The CRI (corresponding to the shortest resting interval that allowed jump height to be maintained for a long time without fatigue) was determined dividing the average external work needed to jump at a fixed height (J) by b parameter (J/s). in the final session, participants jumped at their calculated CRI. A high coefficient of determination (0.995 +/- 0.007) and the CRI (7.5 +/- 1.6 s) were obtained. In addition, the longer the resting period, the greater the number of jumps (44 13, 71 28, 105 30, 169 53 jumps; p<0.0001), time to exhaustion (179 +/- 50, 351 +/- 120, 610 +/- 141, 1,282 +/- 417 s; p<0.0001) and total external work (28.0 +/- 8.3, 45.0 +/- 16.6, 67.6 +/- 17.8, 111.9 +/- 34.6 kJ; p<0.0001). Therefore, the critical power model may be an alternative approach to determine the CRI during intermittent vertical jumps.

Integrablility of a classical N=2 super sinh-Gordon model with jump defects

The Lagrangian formalism for the N = 2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained.The Lax formulation based on the affine super Lie algebra sl(2, 2) within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

Grassmannian and bosonic Thirring models with jump defects

In this paper we discuss the Lax formulation of the Grassmannian and Bosonic Thirring models in the presence of jump defects. For the Grassmannian case, the defect is described by Backlund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the Backlund transformation for the Bosonic Thirring model which is verified by some Backlund transitions like vacuum-one soliton, one soliton-one soliton, one soliton-two solitons and two solitons-two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model with jump defects.

Classical integrable N=1 and N=2 super sinh-Gordon models with jump defects

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the N = 1 and N = 2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions. As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N = 1 case is presented. The resulting integrable models are shown to be invariant under supersymmetric transformation.

High-order upwinding and the hydraulic jump

This work is concerned with the computation of incompressible axisymmetric and fall three-dimensional free-surface flows. In particular, the circular-hydraulic jump is simulated and compared with approximate analytic solutions. However, the principal thrust of this paper is to provide a real problem as a test bed for comparing the many existing convective approximations. Their performance is compared; SMART, HLPA and VONOS emerge as acceptable upwinding methods for this problem. Copyright (C) 2002 John Wiley Sons, Ltd.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.