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941.
942.
We establish the Default Barrier Intensity (DBI) model, based on the conditional survival probability (also called hazard function barrier), which allows the pricing of credit derivatives with stochastic parameters. Moreover, the DBI is an analytic model which combines the structural and the reduced form approaches. It deals with the impact of the default barrier intensity on the processes around the firm. Using this model we prove the Doob–Meyer decomposition of the default process associated with the random barrier. In this framework, we present the default barrier process as the sum of its compensator (which is a predictable process) and a martingale related to the smallest filtration making the random barrier a stopping time. Furthermore, the DBI as well as the Shifted Square Root Diffusion (SSRD) Alfonsi’s model emphasizes on the dependence between the stochastic default intensity and the interest rate. This model can be useful since it can be easily generalized to all the credit derivatives products such as Collateralized Debt Obligations (CDO) and Credit Default Swaps (CDS). 相似文献
943.
We prove the existence of the O-U Dirichlet form and the damped O-U Dirichlet form on path space over a general non-compact Riemannian manifold which is complete and stochastically complete. We show a weighted log-Sobolev inequality for the O-U Dirichlet form and the (standard) log-Sobolev inequality for the damped O-U Dirichlet form. In particular, the Poincaré inequality (and the super Poincaré inequality) can be established for the O-U Dirichlet form on path space over a class of Riemannian manifolds with unbounded Ricci curvatures. Moreover, we construct a large class of quasi-regular local Dirichlet forms with unbounded random diffusion coefficients on path space over a general non-compact manifold. 相似文献
944.
Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more general groups, namely, H-groups by employing the theory of supplementary functions introduced and developed by M.I. Knopp and S.Y. Husseini. In particular, we show that the set of Eichler integrals, which have polynomial period functions, is the same as the set of holomorphic parts of harmonic weak Maass forms of which the non-holomorphic parts are certain period integrals of cusp forms. From this we deduce relations among period functions for harmonic weak Maass forms. 相似文献
945.
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as “coefficients”. A reformulation of the respective problems is constructed such that they turn out to be unitarily equivalent to inverting a maximal monotone relation in a Hilbert space. The method is based on the idea of “tailor‐made” distributions as provided by the construction of extrapolation spaces, see e.g. [Picard, McGhee: Partial Differential Equations: A unified Hilbert Space Approach (De Gruyter, 2011)]. The abstract framework is illustrated by various examples. 相似文献
946.
The linear barycentric rational collocation method for solving heat conduction equation is presented. The matrix form of discrete heat conduction equation by collocation method is also obtained. With the help of convergence rate of the barycentric interpolation, the convergence rate of linear barycentric rational collocation method for solving heat conduction equation is proved. At last, several numerical examples are provided to validate the theoretical analysis. 相似文献
947.
Let V be a finite-dimensional vector space over a finite field and let f be a trilinear alternating form over V. For such forms, we introduce two new invariants. Together with a generalized radical polynomial used for classification of forms in dimension 8 over GF(2), they are sufficient to distinguish between all trilinear alternating forms in dimension 9 over GF(2). To prove the completeness of the list of forms, we computed their groups of automorphisms. There are 31 degenerate and 317 nondegenerate forms. We point out some forms with either small or large automorphism group. 相似文献
948.
Hopf Bifurcation Analysis for a Delayed Business Cycle Model-The Equivalence of Multiple Time Scales Versus Center Manifold Reduction Methods 下载免费PDF全文
In this paper, we study the Hopf bifurcation of a model with a second order term, which is the business cycle model with delay. Multiple time scales method, which is mainly used by the engineering researchers, and center manifold reduction method, which is mainly used by researchers from mathematical society, are used to derive the two types of normal forms near the Hopf critical point. A comparison between the two methods shows that the two normal forms are equivalent. Scholars can derive the normal form by choosing appropriate methods according to their actual demands. Moreover, bifurcation analysis and numerical simulations are given to verify the analytical predictions. 相似文献
949.
研究带反馈的且具有正、负两类顾客的M/M/1/N工作休假排队模型.工作休假策略为空竭服务多重工作休假.负顾客一对一抵消队首正在接受服务的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.完成服务的正顾客以概率p(0
相似文献
950.
利用微分算子及n阶常系数非齐次线性微分方程的特征方程根与系数的关系给出其特解的逐次积分形式,并由此给出自由项f(x)=Pm(x)eλx(其中Pm(x)为m次多项式)时特解的简单递推公式. 相似文献