EXPLICIT SOLUTION PROCESSES FOR NONLINEAR JUMP-DIFFUSION EQUATIONS

被引：0

作者：

Uenal, Gazanfer ^{[1
,2
,3
]}

Turkeri, Hasret ^{[4
]}

Khalique, Chaudry Masood ^{[1
]}

机构：

[1] North West Univ, Int Inst Symmetry Anal & Math Modelling, Dept Math Sci, ZA-2735 Mmabatho, South Africa

[2] Yeditepe Univ, Dept Int Finance, Istanbul, Turkey

[3] Yeditepe Univ, Dept Math, Istanbul, Turkey

[4] Istanbul Tech Univ, Dept Math, TR-80626 Istanbul, Turkey

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2010年 / 17卷 / 03期

关键词：

Compound Poisson processes; linearization conditions; stochastic integrating factor; explicit solution processes; stochastic differential equations; DIFFERENTIAL SUBSTITUTIONS;

D O I：

10.1142/S1402925110000908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce the stochastic integrating factor to solve the linear jump-diffusion equations. Extended Cox-Ingersoll-Ross, Brennan-Schwartz and Epstein models are shown to be linearizable and their explicit solutions are presented.

引用

页码：281 / 310

页数：30

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