Limit theorems for stationary random evolutions

Joseph C. Watkins

doi:10.1016/0304-4149(85)90025-0

Limit theorems for stationary random evolutions

Joseph C. Watkins

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

9 Scopus citations

Abstract

On a separable Banach space, let A(ξ₁),A(ξ₂),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξ_i) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions Y_n(t)=exp 1 nA(ξ_[n²t])⋯exp 1 nA(ξ₂)exp 1 nA(ξ₁)Y_n(0)as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.

Original language	English (US)
Pages (from-to)	189-224
Number of pages	36
Journal	Stochastic Processes and their Applications
Volume	19
Issue number	2
DOIs	https://doi.org/10.1016/0304-4149(85)90025-0
State	Published - Apr 1985
Externally published	Yes

Keywords

central limit theorem
law of large numbers
martingale problem
mixing
random evolution
stationary process

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(85)90025-0

Cite this

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title = "Limit theorems for stationary random evolutions",

abstract = "On a separable Banach space, let A(ξ1),A(ξ2),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξi) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions Yn(t)=exp 1 nA(ξ[n2t])⋯exp 1 nA(ξ2)exp 1 nA(ξ1)Yn(0)as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.",

keywords = "central limit theorem, law of large numbers, martingale problem, mixing, random evolution, stationary process",

author = "Watkins, {Joseph C.}",

note = "Funding Information: I thank John Walsh and the National Science and Engineering Research Council of Canada for supporting my research at the University of British Columbia.",

year = "1985",

month = apr,

doi = "10.1016/0304-4149(85)90025-0",

language = "English (US)",

volume = "19",

pages = "189--224",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "2",

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TY - JOUR

T1 - Limit theorems for stationary random evolutions

AU - Watkins, Joseph C.

N1 - Funding Information: I thank John Walsh and the National Science and Engineering Research Council of Canada for supporting my research at the University of British Columbia.

PY - 1985/4

Y1 - 1985/4

N2 - On a separable Banach space, let A(ξ1),A(ξ2),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξi) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions Yn(t)=exp 1 nA(ξ[n2t])⋯exp 1 nA(ξ2)exp 1 nA(ξ1)Yn(0)as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.

AB - On a separable Banach space, let A(ξ1),A(ξ2),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξi) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions Yn(t)=exp 1 nA(ξ[n2t])⋯exp 1 nA(ξ2)exp 1 nA(ξ1)Yn(0)as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.

KW - central limit theorem

KW - law of large numbers

KW - martingale problem

KW - mixing

KW - random evolution

KW - stationary process

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U2 - 10.1016/0304-4149(85)90025-0

DO - 10.1016/0304-4149(85)90025-0

M3 - Article

AN - SCOPUS:30244522523

SN - 0304-4149

VL - 19

SP - 189

EP - 224

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Limit theorems for stationary random evolutions

Abstract

Keywords

ASJC Scopus subject areas

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