694 research outputs found

    Calculating multivariate ruin probabilities via Gaver–Stehfest inversion technique.

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    Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver–Stehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literatureMultivariate ultimate ruin probability; Laplace transform; Integral equations; Numerical methods;

    Laplace deconvolution on the basis of time domain data and its application to Dynamic Contrast Enhanced imaging

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    In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Due to this triangular structure, there is a common number mm of terms in the function expansions to control, which is realized via complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut-off at TT and provides an estimator with the risk within a logarithmic factor of the oracle risk. We emphasize that, in the present paper, we consider the true observational model with possibly nonequispaced observations which are available on a finite interval of length TT which appears in many different contexts, and account for the bias associated with this model (which is not present when T→∞T\rightarrow\infty). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of micro-circulation within tissues such as cancerous tumors. Presence of a tuning parameter aa allows to choose the most advantageous time units, so that both the kernel and the unknown right hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast, efficient, accurate, usable from a practical point of view and very competitive.Comment: 36 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1207.223

    Laguerre polynomials and the inverse Laplace transform using discrete data

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    We consider the problem of finding a function defined on (0,∞)(0,\infty) from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials to convert the problem in an analytic interpolation problem. Then, using the coefficients of Lagrange polynomials we shall construct a stable approximation solution.Comment: 14 page

    Weakly nonlinear circuit analysis based on fast multidimensional inverse Laplace transform

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    There have been continuing thrusts in developing efficient modeling techniques for circuit simulation. However, most circuit simulation methods are time-domain solvers. In this paper we propose a frequency-domain simulation method based on Laguerre function expansion. The proposed method handles both linear and nonlinear circuits. The Laguerre method can invert multidimensional Laplace transform efficiently with a high accuracy, which is a key step of the proposed method. Besides, an adaptive mesh refinement (AMR) technique is developed and its parallel implementation is introduced to speed up the computation. Numerical examples show that our proposed method can accurately simulate large circuits while enjoying low computation complexity. © 2012 IEEE.published_or_final_versio
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