量值仿射和多项式扩散

IF 1.1 2区 数学 Q3 STATISTICS & PROBABILITY
Christa Cuchiero , Luca Di Persio , Francesco Guida , Sara Svaluto-Ferro
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引用次数: 0

摘要

我们引入了一类量值过程,与它们的有限维对应过程类似,这些过程将被称为量值多项式扩散。我们展示了所谓的矩公式,即通过有限维线性 PDEs 系统来表示条件边际矩。此外,我们还描述了相应无穷小生成器的特征,从而在其域足够大的情况下,获得了类似于多项式扩散的表示。一般来说,无限维设置允许严格超出这一表示的更丰富的规范。作为一种特例,我们恢复了度量值仿射扩散,有时也称为道森-瓦塔那比超过程。从数学金融学的角度来看,多项式框架尤其具有吸引力,因为它可以将许多著名的有限维模型及其可操作性转移到无限维的量值环境中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Measure-valued affine and polynomial diffusions

We introduce a class of measure-valued processes, which – in analogy to their finite dimensional counterparts – will be called measure-valued polynomial diffusions. We show the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs. Furthermore, we characterize the corresponding infinitesimal generators obtaining a representation analogous to polynomial diffusions on R+m, in cases where their domain is large enough. In general the infinite dimensional setting allows for richer specifications strictly beyond this representation. As a special case, we recover measure-valued affine diffusions, sometimes also called Dawson–Watanabe superprocesses. From a mathematical finance point of view, the polynomial framework is especially attractive since it allows to transfer many famous finite dimensional models and their tractability properties to an infinite dimensional measure-valued setting.

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来源期刊
Stochastic Processes and their Applications
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.
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