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06831cam a2200901Mi 4500 |
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ocn772845223 |
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OCoLC |
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20240925133555.0 |
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m d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr |n|---||||| |
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120116s2012 gw a ob 001 0 eng d |
| 010 ## - LIBRARY OF CONGRESS CONTROL NUMBER |
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2011036413 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
EBLCP |
| Language of cataloging |
eng |
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pn |
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EBLCP |
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OCLCQ |
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| 019 ## - |
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785776485 |
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961527204 |
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979584734 |
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985273235 |
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1388226056 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783110258165 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
3110258161 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
3110258692 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783110258691 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783110559149 |
| Qualifying information |
(electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
3110559145 |
| Qualifying information |
(electronic bk.) |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.1515/9783110258165 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
2747065 |
| -- |
(N$T) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
430094 |
| -- |
(N$T) |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)772845223 |
| Canceled/invalid control number |
(OCoLC)785776485 |
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(OCoLC)961527204 |
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(OCoLC)979584734 |
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(OCoLC)985273235 |
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(OCoLC)985390879 |
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(OCoLC)988416544 |
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(OCoLC)988476448 |
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(OCoLC)991924826 |
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(OCoLC)994927097 |
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(OCoLC)1013184144 |
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(OCoLC)1018005982 |
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(OCoLC)1037712939 |
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(OCoLC)1038654813 |
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(OCoLC)1038688029 |
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(OCoLC)1055401727 |
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(OCoLC)1058126024 |
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(OCoLC)1059082058 |
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(OCoLC)1064747765 |
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(OCoLC)1081293925 |
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(OCoLC)1096236715 |
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(OCoLC)1119122738 |
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(OCoLC)1152986076 |
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(OCoLC)1162004094 |
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(OCoLC)1264840415 |
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(OCoLC)1290043454 |
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(OCoLC)1300495312 |
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(OCoLC)1388226056 |
| 037 ## - SOURCE OF ACQUISITION |
|---|
| Stock number |
835465 |
| Source of stock number/acquisition |
Proquest Ebook Central |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA314 .M484 2011 |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT |
| Subject category code subdivision |
005000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
|---|
| Subject category code |
MAT |
| Subject category code subdivision |
034000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.83 |
| 084 ## - OTHER CLASSIFICATION NUMBER |
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| Classification number |
SK 950 |
| Number source |
rvk |
| 049 ## - LOCAL HOLDINGS (OCLC) |
|---|
| Holding library |
MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Meerschaert, Mark M., |
| Dates associated with a name |
1955- |
| 9 (RLIN) |
175337 |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Stochastic models for fractional calculus / |
| Statement of responsibility, etc. |
Mark M. Meerschaert, Alla Sikorskii. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
|---|
| Place of publication, distribution, etc. |
Berlin : |
| Name of publisher, distributor, etc. |
De Gruyter, |
| Date of publication, distribution, etc. |
©2012. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 online resource (x, 294 pages) : |
| Other physical details |
illustrations |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
|---|
| File type |
data file |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
De Gruyter studies in mathematics, |
| International Standard Serial Number |
0179-0986 ; |
| Volume/sequential designation |
43 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc |
Includes bibliographical references (pages 279-288), and index. |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Title |
Introduction ; |
| -- |
The traditional diffusion model -- |
| -- |
Fractional diffusion -- |
| -- |
Fractional derivatives ; |
| -- |
The Grünwald formula -- |
| -- |
More fractional derivatives -- |
| -- |
The Caputo derivative -- |
| -- |
Time-fractional diffusion -- |
| -- |
Stable limit distributions ; |
| -- |
Infinitely divisible laws -- |
| -- |
Stable characteristic functions -- |
| -- |
Semigroups -- |
| -- |
Poisson approximation -- |
| -- |
Shifted Poisson approximation -- |
| -- |
Triangular arrays -- |
| -- |
One-sided stable limits -- |
| -- |
Two-sided stable limits -- |
| -- |
Continuous time random walks ; |
| -- |
Regular variation -- |
| -- |
Stable central limit theorem -- |
| -- |
Continuous time random walks -- |
| -- |
Convergence in Skorokhod space -- |
| -- |
CTRW governing equations -- |
| -- |
Computations in R ; |
| -- |
R codes for fractional diffusion -- |
| -- |
Sample path simulations |
| 505 00 - FORMATTED CONTENTS NOTE |
|---|
| Title |
Vector fractional diffusion ; |
| -- |
Vector random walks -- |
| -- |
Vector random walks with heavy tails -- |
| -- |
Triangular arrays of random vectors -- |
| -- |
Stable random vectors -- |
| -- |
Vector fractional diffusion equation -- |
| -- |
Operator stable laws -- |
| -- |
Operator regular variation -- |
| -- |
Generalized domains of attraction -- |
| -- |
Applications and extensions ; |
| -- |
LePage series representation -- |
| -- |
Tempered stable laws -- |
| -- |
Tempered fractional derivatives -- |
| -- |
Pearson diffusions -- |
| -- |
Fractional Pearson diffusions -- |
| -- |
Fractional Brownian motion -- |
| -- |
Fractional random fields -- |
| -- |
Applications of fractional diffusion -- |
| -- |
Applications of vector fractional diffusion. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. |
| 588 0# - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Print version record. |
| 546 ## - LANGUAGE NOTE |
|---|
| Language note |
In English. |
| 590 ## - LOCAL NOTE (RLIN) |
|---|
| Local note |
OCLC control number change |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Fractional calculus. |
| 9 (RLIN) |
73917 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Diffusion processes. |
| 9 (RLIN) |
70248 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Stochastic analysis. |
| 9 (RLIN) |
3834 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Dérivées fractionnaires. |
| 9 (RLIN) |
969833 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Processus de diffusion. |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Analyse stochastique. |
| 9 (RLIN) |
12283 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Calculus. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
71168 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
MATHEMATICS |
| General subdivision |
Mathematical Analysis. |
| Source of heading or term |
bisacsh |
| 9 (RLIN) |
71169 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Diffusion processes. |
| Source of heading or term |
fast |
| Authority record control number |
(OCoLC)fst00893561 |
| 9 (RLIN) |
70248 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Fractional calculus. |
| Source of heading or term |
fast |
| Authority record control number |
(OCoLC)fst00933515 |
| 9 (RLIN) |
73917 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Stochastic analysis. |
| Source of heading or term |
fast |
| Authority record control number |
(OCoLC)fst01133499 |
| 9 (RLIN) |
3834 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Stochastische Analysis |
| Source of heading or term |
gnd |
| 9 (RLIN) |
3837 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Anomale Diffusion |
| Source of heading or term |
gnd |
| 9 (RLIN) |
9277 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Gebrochene Analysis |
| Source of heading or term |
gnd |
| 9 (RLIN) |
615126 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Gebrochene Analysis. |
| Source of heading or term |
idszbz |
| 9 (RLIN) |
615126 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Stochastische Analysis. |
| Source of heading or term |
idszbz |
| 9 (RLIN) |
3837 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Stochastisches Modell. |
| Source of heading or term |
idszbz |
| 9 (RLIN) |
35218 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Diffusion. |
| Source of heading or term |
idszbz |
| 9 (RLIN) |
9275 |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Sikorskii, Alla., |
| Relator term |
author. |
| 9 (RLIN) |
615127 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| Main entry heading |
Meerschaert, Mark M., 1955- |
| Title |
Stochastic models for fractional calculus. |
| Place, publisher, and date of publication |
Berlin : De Gruyter, ©2011 |
| International Standard Book Number |
9783110258691 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
De Gruyter studies in mathematics ; |
| Volume number/sequential designation |
43. |
| International Standard Serial Number |
0179-0986 |
| 9 (RLIN) |
398321 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
EBSCOhost |
| Uniform Resource Identifier |
<a href="https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430094">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=430094</a> |
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Askews and Holts Library Services |
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ASKH |
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AH25311050 |
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De Gruyter |
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DEGR |
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9783110258165 |
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EBL - Ebook Library |
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EBLB |
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EBL835465 |
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ebrary |
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EBRY |
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ebr10527867 |
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EBSCOhost |
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EBSC |
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430094 |
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ProQuest MyiLibrary Digital eBook Collection |
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IDEB |
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cis28650986 |
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YBP Library Services |
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YANK |
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7310901 |
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92 |
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N$T |