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

E. A. Feinberg; A. N. Shiryaev

doi:10.1137/S0040585X97T991684

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

E. A. Feinberg
, A. N. Shiryaev

Applied Mathematics and Statistics

Steklov Mathematical Institute of RAS

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	643-656
Number of pages	14
Journal	Theory of Probability and its Applications
Volume	68
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97T991684
State	Published - 2024

Keywords

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

Access to Document

10.1137/S0040585X97T991684

Cite this

@article{bd4e57a3e4fa41f9acbac641f2bab3ba,

title = "ON FORWARD AND BACKWARD KOLMOGOROV EQUATIONS FOR PURE JUMP MARKOV PROCESSES AND THEIR GENERALIZATIONS",

abstract = "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.",

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

author = "Feinberg, \{E. A.\} and Shiryaev, \{A. N.\}",

year = "2024",

doi = "10.1137/S0040585X97T991684",

language = "English",

volume = "68",

pages = "643--656",

journal = "Theory of Probability and its Applications",

issn = "0040-585X",

number = "4",

}

TY - JOUR

T1 - ON FORWARD AND BACKWARD KOLMOGOROV EQUATIONS FOR PURE JUMP MARKOV PROCESSES AND THEIR GENERALIZATIONS

AU - Feinberg, E. A.

AU - Shiryaev, A. N.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - differentiability of the transition probability

KW - finite and countable state spaces

KW - forward and backward equations

KW - pure jump Markov process

KW - standard Borel space

KW - uniqueness of the solution

UR - https://www.scopus.com/pages/publications/85185273157

U2 - 10.1137/S0040585X97T991684

DO - 10.1137/S0040585X97T991684

M3 - Article

AN - SCOPUS:85185273157

SN - 0040-585X

VL - 68

SP - 643

EP - 656

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 4

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this