On the independence of the value function for stochastic differential games of the probability space

N. V. Krylov

doi:10.1016/j.spa.2014.07.021

On the independence of the value function for stochastic differential games of the probability space

N. V. Krylov

School of Mathematics

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

1 Scopus citations

Abstract

We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,ℱ) but introduce probability measures by means of Girsanov's transformation depending on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.

Original language	English (US)
Pages (from-to)	4224-4243
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	124
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2014.07.021
State	Published - Dec 2014

Bibliographical note

Funding Information:
The author is sincerely grateful to the referee who raised an important question now addressed in the introduction. The author was partially supported by NSF Grant DMS-1160569 .

Keywords

Isaacs equation
Stochastic differential games
Value functions

Publisher link

10.1016/j.spa.2014.07.021

Find It

Find It at U of M Libraries

Cite this

@article{45006348041c4b06a8e61fee4ecbd763,

title = "On the independence of the value function for stochastic differential games of the probability space",

abstract = "We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,ℱ) but introduce probability measures by means of Girsanov's transformation depending on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.",

keywords = "Isaacs equation, Stochastic differential games, Value functions",

author = "Krylov, {N. V.}",

note = "Funding Information: The author is sincerely grateful to the referee who raised an important question now addressed in the introduction. The author was partially supported by NSF Grant DMS-1160569 . ",

year = "2014",

month = dec,

doi = "10.1016/j.spa.2014.07.021",

language = "English (US)",

volume = "124",

pages = "4224--4243",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier",

number = "12",

}

TY - JOUR

T1 - On the independence of the value function for stochastic differential games of the probability space

AU - Krylov, N. V.

N1 - Funding Information: The author is sincerely grateful to the referee who raised an important question now addressed in the introduction. The author was partially supported by NSF Grant DMS-1160569 .

PY - 2014/12

Y1 - 2014/12

N2 - We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,ℱ) but introduce probability measures by means of Girsanov's transformation depending on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.

AB - We show that the value function in a stochastic differential game does not change if we keep the same space (Ω,ℱ) but introduce probability measures by means of Girsanov's transformation depending on the policies of the players. We also show that the value function does not change if we allow the driving Wiener processes to depend on the policies of the players. Finally, we show that the value function does not change if we perform a random time change with the rate depending on the policies of the players.

KW - Isaacs equation

KW - Stochastic differential games

KW - Value functions

UR - http://www.scopus.com/inward/record.url?scp=84906691337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906691337&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2014.07.021

DO - 10.1016/j.spa.2014.07.021

M3 - Article

AN - SCOPUS:84906691337

SN - 0304-4149

VL - 124

SP - 4224

EP - 4243

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -

On the independence of the value function for stochastic differential games of the probability space

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this