We consider first passage times for piecewise exponential Markov processes that may be viewed as Ornstein-Uhlenbeck processes driven by compound Poisson processes. We allow for two-sided jumps and as a main result we derive the joint Laplace transform of the first passage time of a lower level and the resulting undershoot when passage happens as a consequence of a downward (negative) jump. The Laplace transform is determined using complex contour integrals and we illustrate how the choice of contours depends in a crucial manner on the particular form of the negative jump part, which is allowed to belong to a dense class of probabilities. We give extensions of the main result to two-sided exit problems where the negative jumps are as before but now it is also required that the positive jumps have a distribution of the same type. Further, extensions are given for the case where the driving Lévy process is the sum of a compound Poisson process and an independent Brownian motion. Examples are used to illustrate the theoretical results and include the numerical evaluation of some concrete exit probabilities. Also, some of the examples show that for specific values of the model parameters it is possible to obtain closed form expressions for the Laplace transform, as is the case when residue calculus may be used for evaluating the relevant contour integrals.

The Dogue de Bordeaux may be highly predisposed to aortic stenosis. The small aortic annulus noted in healthy and affected Dogue de Bordeaux and a decreased aortoseptal angle noted in affected dogs in this study might reflect key aetiological features in the development of aortic stenosis.

SummaryReasons for performing study: Equine lameness examination is based on subjective visual scoring of lameness. Instrumented objective methods for lameness examinations may be complicated to perform and the equipment is often stationary. Accelerometry has a potential clinical use; however, the reduction and interpretation of equine accelerometric data are not yet routine and the value of accelerometry in equine lameness examination is unclear. Objectives: To use accelerometric data to calculate 2 different accelerometric symmetry scores and to evaluate the agreement of these with traditional lameness scores done by experienced equine practitioners. Methods: Six sound horses were equipped with a 3 axis 10G piezoresistant accelerometer at the lowest point of the back. Horses were trotted and video recorded at 0, 3, 15, 30, 45 and 60 min after injection of saline into one metacarpophalangeal joint. Video recordings were scored in a blind manner according to the AAEP scale by 2 experienced practitioners. Interobserver agreements and 2 symmetry scores S and A, developed on the basis of Fourier transformation of the obtained accelerometric data, were calculated and regression analysis between AAEP scores and symmetry scores was performed. Results: Interobserver agreements were 70%. There was a statistically significant relationship between AAEP lameness scores and both symmetry scores. Conclusions: Both symmetry scores showed a significant relationship with the AAEP scores and can be a valuable tool in the detection and quantification of lameness. While the S score was able to detect changes in degree of lameness, the A score was capable of detecting the lame diagonal. However, more research is needed for the development of a combined accelerometric score to take advantage of the strengths of each of the symmetry scores.

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In this paper we study the behavior of GARCH(1,1) parameter estimates when data is generated by certain types of stochastic volatility models including well known models from the literature on realized volatility and mathematical finance. Our main result states that the parameter estimates (a,b) tend to (0,1) as the sampling frequency is increased thereby establishing that the stochastic sequence of QMLEs do indeed behave as the deterministic parameters considered in the literature on filtering based on misspecified ARCH models, see e.g. Nelson (1992). The convergence result is in line with the empirical finding that a GARCH model fitted to virtually any financial data set exhibits the property that a+b tends to one, a fact commonly referred to as the IGARCH effect. Hence, the paper suggests that the IGARCH effect could be caused by misspecification. An included study of simulations and empirical high frequency data is found to be in very good accordance with the mathematical results.