全纯jump-diffusions

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-09-24 DOI:10.1016/j.spa.2025.104781

Christa Cuchiero , Francesca Primavera , Sara Svaluto-Ferro

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引用次数: 0

摘要

我们引入了一类跳跃扩散，称为全纯，其中众所周知的仿射和多项式过程是它的特殊实例。定义属性涉及扩展生成器，它需要将全纯函数（子集）映射到自身。这导致通过潜在的无限维线性ODE表示过程边际的幂级数的期望。我们用同样的方法考虑全纯函数的指数，得到了一类被称为仿射全纯的过程，给出了量作为幂级数特征函数的表示。依靠复分析的有力结果，我们得到了保证全纯和仿射全纯性质的过程特征的充分条件，并为几类跳跃扩散提供了应用。

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Holomorphic jump-diffusions

We introduce a class of jump-diffusions, called holomorphic, of which the well-known classes of affine and polynomial processes are particular instances. The defining property concerns the extended generator, which is required to map a (subset of) holomorphic functions to themselves. This leads to a representation of the expectation of power series of the process’ marginals via a potentially infinite dimensional linear ODE. We apply the same procedure by considering exponentials of holomorphic functions, leading to a class of processes named affine-holomorphic for which a representation for quantities as the characteristic function of power series is provided. Relying on powerful results from complex analysis, we obtain sufficient conditions on the process’ characteristics which guarantee the holomorphic and affine-holomorphic properties and provide applications to several classes of jump-diffusions.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.