ON FORWARD AND BACKWARD KOLMOGOROV EQUATIONS FOR PURE JUMP MARKOV PROCESSES AND THEIR GENERALIZATIONS

被引：0

作者：

Feinberg, E. A. ^{[1
]}

Shiryaev, A. N. ^{[2
]}

机构：

[1] SUNY Stony Brook, Dept Appl Math & Stat, Stony Brook, NY 11794 USA

[2] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2023年 / 68卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

pure jump Markov process; finite and countable state spaces; standard Borel space; differentiability of the transition probability; forward and backward equations; uniqueness of the solution;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the present paper, we first give a survey of the forward and backward Kolmogorov equations for pure jump Markov processes with finite and countable state spaces, and then describe relevant results for the case of Markov processes with values in standard Borel spaces based on results of W. Feller and the authors of the present paper.

引用

页码：643 / 656

页数：14

共 50 条

[31] Estimating Equations for Density Dependent Markov Jump Processes
Odubote, Oluseyi
Linder, Daniel F.
MATHEMATICS, 2021, 9 (04) : 1 - 16
[32] Option Pricing for Pure Jump Processes with Markov Switching Compensators
Robert J. Elliott
Carlton-James U. Osakwe
Finance and Stochastics, 2006, 10 : 250 - 275
[33] Option pricing for pure jump processes with Markov switching compensators
Elliott, RJ
Osakwe, CJU
FINANCE AND STOCHASTICS, 2006, 10 (02) : 250 - 275
[34] SPEED OF CONVERGENCE OF A SEQUENCE OF PURE JUMP MARKOV-PROCESSES
ALLAIN, MF
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (17): : 1015 - 1018
[35] ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS
Bao, Feng
Cao, Yanzhao
Chi, Hongmei
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 2019, 9 (02) : 143 - 159
[36] Importance sampling for Kolmogorov backward equations
Hermann Singer
AStA Advances in Statistical Analysis, 2014, 98 : 345 - 369
[37] Importance sampling for Kolmogorov backward equations
Singer, Hermann
ASTA-ADVANCES IN STATISTICAL ANALYSIS, 2014, 98 (04) : 345 - 369
[38] A mean-field maximum principle for optimal control of forward–backward stochastic differential equations with Poisson jump processes
Hafayed M.
Hafayed, Mokhtar (hafayedmokhtar@yahoo.com), 2013, Springer Science and Business Media Deutschland GmbH (01) : 300 - 315
[39] Risk measures for derivatives with Markov-modulated pure jump processes
Elliott R.J.
Chan L.
Siu T.K.
Asia-Pacific Financial Markets, 2006, 13 (2) : 129 - 149
[40] Safety Verification of Continuous-Space Pure Jump Markov Processes
Soudjani, Sadegh Esmaeil Zadeh
Majumdar, Rupak
Abate, Alessandro
TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS (TACAS 2016), 2016, 9636 : 147 - 163

← 1 2 3 4 5 →