Stochastic calculus for symmetric markov processes

Z. Q. Chen; P. J. Fitzsimmons; K. Kuwae; T. S. Zhang

doi:10.1214/07-AOP347

Stochastic calculus for symmetric markov processes

Z. Q. Chen^*, P. J. Fitzsimmons, K. Kuwae, T. S. Zhang

^*Corresponding author for this work

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

39 Citations (Scopus)

Abstract

Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

Original language	English
Pages (from-to)	931-970
Number of pages	40
Journal	Annals of Probability
Volume	36
Issue number	3
DOIs	https://doi.org/10.1214/07-AOP347
Publication status	Published - May 2008
Externally published	Yes

Keywords

Additive functional
Dual additive functional
Dual predictable projection
Generalized itô formula
Martingale additive functional
Revuz measure
Symmetric markov process
Time reversal, stochastic integral

Access to Document

10.1214/07-AOP347

Cite this

@article{89fed7dcb2944c00a57ab38e39d8ae93,

title = "Stochastic calculus for symmetric markov processes",

abstract = "Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an It{\^o} formula for Dirichlet processes is obtained.",

keywords = "Additive functional, Dual additive functional, Dual predictable projection, Generalized it{\^o} formula, Martingale additive functional, Revuz measure, Symmetric markov process, Time reversal, stochastic integral",

author = "Chen, {Z. Q.} and Fitzsimmons, {P. J.} and K. Kuwae and Zhang, {T. S.}",

year = "2008",

month = may,

doi = "10.1214/07-AOP347",

language = "English",

volume = "36",

pages = "931--970",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Statistics",

number = "3",

}

TY - JOUR

T1 - Stochastic calculus for symmetric markov processes

AU - Chen, Z. Q.

AU - Fitzsimmons, P. J.

AU - Kuwae, K.

AU - Zhang, T. S.

PY - 2008/5

Y1 - 2008/5

N2 - Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

AB - Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

KW - Additive functional

KW - Dual additive functional

KW - Dual predictable projection

KW - Generalized itô formula

KW - Martingale additive functional

KW - Revuz measure

KW - Symmetric markov process

KW - Time reversal, stochastic integral

UR - http://www.scopus.com/inward/record.url?scp=51949089451&partnerID=8YFLogxK

U2 - 10.1214/07-AOP347

DO - 10.1214/07-AOP347

M3 - Article

AN - SCOPUS:51949089451

SN - 0091-1798

VL - 36

SP - 931

EP - 970

JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Stochastic calculus for symmetric markov processes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this