Analytical methods for Markov semigroups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2007
|
| Schriftenreihe: | Pure and applied mathematics
283 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 511-522) and index |
| Beschreibung: | XXXI, 526 S. 24 cm |
| ISBN: | 1584886595 9781584886594 |
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| 245 | 1 | 0 | |a Analytical methods for Markov semigroups |c Luca Lorenzi ; Marcello Bertoldi |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2007 | |
| 300 | |a XXXI, 526 S. |c 24 cm | ||
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| 490 | 1 | |a Pure and applied mathematics |v 283 | |
| 500 | |a Includes bibliographical references (p. 511-522) and index | ||
| 650 | 4 | |a Markov, Processus de | |
| 650 | 4 | |a Semi-groupes | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Semigroups | |
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Datensatz im Suchindex
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| adam_text | ANALYTICAL METHODS FOR MARKOV SEMIGROUPS LUCA LORENZI UNIVERSITY OF
PARMA PARMA, ITALY MARCELLO BERTOLDI BANCA INTESA MILANO, ITALY CHAPMAN
&. HALL/CRC TAYLOR F» FRANCIS CROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA
BUSINESS CONTENTS 1 INTRODUCTION XVII 1 MARKOV SEMIGROUPS IN W N 1 2 THE
ELLIPTIC EQUATION AND THE CAUCHY PROBLEM IN CB(M. N ): THE UNIFORMLY
ELLIPTIC CASE 3 2.0 INTRODUCTION 3 2.1 THE ELLIPTIC EQUATION AND THE
RESOLVENT R(X) 7 2.2 THE CAUCHY PROBLEM AND THE SEMIGROUP 10 2.3 THE
WEAK GENERATOR OF T(T) 21 2.4 THE MARKOV PROCESS 27 2.5 THE ASSOCIATED
STOCHASTIC DIFFERENTIAL EQUATION 30 3 ONE-DIMENSIONAL THEORY 33 3.0
INTRODUCTION 33 3.1 THE HOMOGENEOUS EQUATION 34 3.2 THE NONHOMOGENEOUS
EQUATION 41 4 UNIQUENESS RESULTS, CONSERVATION OF PROBABILITY AND MAXI-
MUM PRINCIPLES 51 4.0 INTRODUCTION 51 4.1 CONSERVATION OF PROBABILITY
AND UNIQUENESS 53 4.1.1 MAXIMUM PRINCIPLES 55 4.1.2 THE CASE WHEN C = 0
62 4.2 NONUNIQUENESS 65 5 PROPERTIES OF {T(T)} IN SPACES OF CONTINUOUS
FUNCTIONS 67 5.0 INTRODUCTION 67 5.1 COMPACTNESS OF {T(T)} 68 5.1.1 THE
CONSERVATIVE CASE 69 5.1.2 THE NONCONSERVATIVE CASE 83 5.2 ON THE
INCLUSION T{T){C B (R N )) C C 0 (R N ) 85 5.3 INVARIANCEOF C 0 (R N )
91 6 UNIFORM ESTIMATES FOR THE DERIVATIVES OF T(T)F 95 6.0 INTRODUCTION
95 6.1 UNIFORM ESTIMATES 96 VLLL 6.2 SOME CONSEQUENCES 113 7 POINTWISE
ESTIMATES FOR THE DERIVATIVES OF T(T)F 123 7.0 INTRODUCTION 123 7.1 THE
FIRST TYPE OF POINTWISE GRADIENT ESTIMATES 124 7.2 THE SECOND TYPE OF
POINTWISE GRADIENT ESTIMATES 136 7.3 FURTHER ESTIMATES IOR A = A + Y^J =
IBJ(X)DJ 150 8 INVARIANT MEASURES /I AN D THE SEMIGROUP IN L P (R N ,/I)
155 8.0 INTRODUCTION 155 8.1 EXISTENCE, UNIQUENESS AND GENERAL
PROPERTIES 158 8.1.1 GENERAL PROPERTIES AND UNIQUENESS OF THE INVARIANT
MEA- SURE OF {T(T)} 158 8.1.2 EXISTENCE BY KHAS MINSKII THEOREM 168
8.1.3 EXISTENCE BY COMPACTNESS IN CB(R N ) 175 8.1.4 EXISTENCE BY
SYMMETRY 180 8.2 REGULARITY PROPERTIES OF INVARIANT MEASURES 185 8.2.1
GLOBAL ^-REGULARITY OF THE DENSITY P 191 8.2.2 GLOBAL SOBOLEV REGULARITY
198 8.3 SOME CONSEQUENCES OF THE ESTIMATES OF CHAPTER 6 207 8.4 THE
CONVEX CASE 211 8.5 COMPACTNESS OF T(T) AND OF THE EMBEDDING W^ P C L^
... 214 8.6 THE POINCARE INEQUALITY AND THE SPECTRAL GAP 218 8.7 THE
LOGARITHMIC SOBOLEV INEQUALITY AND HYPERCONTRACTIVITY . 221 9 THE
ORNSTEIN-UHLENBECK OPERATOR 233 9.0 INTRODUCTION 233 9.1 THE FORMULA FOR
T(T)F 235 9.2 PROPERTIES OF {T(T)} IN C B (R N ) 238 9.3 THE INVARIANT
MEASURE /I AN D THE SEMIGROUP IN L^ 243 9.3.1 THE DOMAIN OF THE
REALIZATION OF {T(T)} IN L^R 1 *) . . 254 9.3.2 THE SPECTRUM OF THE
ORNSTEIN-UHLENBECK OPERATOR IN L 264 9.3.3 THE SECTOR OF ANALYTICITY OF
THE ORNSTEIN-UHLENBECK OP- ERATOR IN L 274 9.3.4 HERMITE POLYNOMIALS
276 9.4 THE ORNSTEIN-UHLENBECK OPERATOR IN L P (R N ) 279 10 A CLASS OF
NONANALYTIC MARKOV SEMIGROUPS IN C(,(1 N ) AND IN L (R N ,IJ.) 283 10.0
INTRODUCTION 283 10.1 NONANALYTIC SEMIGROUPS IN CB{R N ) 283 10.2
NONANALYTIC SEMIGROUPS IN L P (R N ,FI) 291 11 MARKOV SEMIGROUPS IN
UNBOUNDED OPEN SETS 297 11 THE CAUCHY-DIRICHLET PROBLEM 299 11.0
INTRODUCTION 299 11.1 TWO MAXIMUM PRINCIPLES 301 11.2 EXISTENCE AND
UNIQUENESS OF THE CLASSICAL SOLUTION 305 11.3 GRADIENT ESTIMATES 308
11.3.1 A PRIORI GRADIENT ESTIMATES 309 11.3.2 AN AUXILIARY PROBLEM 315
11.3.3 PROOF OF THEOREM 11.3.4 324 11.3.4 A COUNTEREXAMPLE TO THE
GRADIENT ESTIMATES 325 12 THE CAUCHY-NEUMANN PROBLEM: THE CONVEX CASE
329 12.0 INTRODUCTION 329 12.1 CONSTRUCTION OF THE SEMIGROUP AND UNIFORM
GRADIENT ESTIMATES 332 12.2 SOME CONSEQUENCES OF THE UNIFORM GRADIENT
ESTIMATES .... 344 12.3 POINTWISE GRADIENT ESTIMATES AND THEIR
CONSEQUENCES 349 12.4 THE INVARIANT MEASURE OF THE SEMIGROUP 357 13 THE
CAUCHY-NEUMANN PROBLEM: THE NONCONVEX CASE 367 13.0 INTRODUCTION 367
13.1 THE CASE OF BOUNDED DIFFUSION COEFFICIENTS 369 13.1.1 A PRIORI
ESTIMATE 371 13.1.2 EXISTENCE OF THE SOLUTION TO PROBLEM (13.0.2) AND
UNI- FORM GRADIENT ESTIMATES 375 13.2 THE CASE WHEN FT IS AN EXTERIOR
DOMAIN 388 13.3 POINTWISE GRADIENT ESTIMATES AND THEIR CONSEQUENCES 394
13.4 THE INVARIANT MEASURE OF THE SEMIGROUP 402 13.5 FINAL REMARKS 404
III A CLASS OF MARKOV SEMIGROUPS IN R ASSOCIATED WITH DEGENERATE
ELLIPTIC OPERATORS 405 14 THE CAUCHY PROBLEM IN C B (R N ) 407 14.0
INTRODUCTION 407 14.1 SOME PRELIMINARY RESULTS ON THE OPERATOR A 409
14.2 EXISTENCE, UNIQUENESS RESULTS AND UNIFORM ESTIMATES 415 14.2.1 SOME
PRELIMINARY LEMMATA 416 14.2.2 UNIFORM ESTIMATES FOR THE SPACE
DERIVATIVES OF THE AP- PROXIMATING SEMIGROUPS {T E (T)} 419 14.2.3
CONSTRUCTION OF THE SEMIGROUP 431 14.3 SOME REMARKABLE PROPERTIES OF THE
SEMIGROUP 439 14.4 THE NONHOMOGENEOUS ELLIPTIC EQUATION 444 IV
APPENDICES 465 A BASIC NOTIONS OF FUNCTIONAL ANALYSIS IN BANACH SPACES
467 A.I BOUNDED, COMPACT AND CLOSED LINEAR OPERATORS 467 A.2 VECTOR
VALUED RIEMANN INTEGRAL 468 A.3 SPECTRUM AND RESOLVENT 470 A.4 SOME
RESULTS FROM INTERPOLATION THEORY 473 B AN OVERVIEW ON STRONGLY
CONTINUOUS AND ANALYTIC SEMIGROUPS 477 B.I STRONGLY CONTINUOUS
SEMIGROUPS 477 B.I.I ON THE CLOSURE OF THE SUM OF GENERATORS OF STRONGLY
CON- TINUOUS SEMIGROUPS 480 B.2 ANALYTIC SEMIGROUPS 482 C PDE S AND
ANALYTIC SEMIGROUPS 487 C.I A PRIORI ESTIMATES 487 C.2 CLASSICAL MAXIMUM
PRINCIPLES 494 C.3 EXISTENCE OF CLASSICAL SOLUTION TO PDE S AND ANALYTIC
SEMI- GROUPS 495 D SOME PROPERTIES OF THE DISTANCE FUNCTION 501 E
FUNCTION SPACES: DEFINITIONS AND MAIN PROPERTIES 505 E.I SPACES OF
FUNCTIONS THAT ARE CONTINUOUS OR HOLDER CONTINUOUS IN DOMAINS QCL 505
E.I.I ISOTROPIC SPACES 505 E.I.2 ANISOTROPIC HOLDER SPACES IN R N 506
E.2 PARABOLIC HOLDER SPACES 508 E.3 L P AND SOBOLEV SPACES 509
REFERENCES 511 INDEX 523
|
| adam_txt |
ANALYTICAL METHODS FOR MARKOV SEMIGROUPS LUCA LORENZI UNIVERSITY OF
PARMA PARMA, ITALY MARCELLO BERTOLDI BANCA INTESA MILANO, ITALY CHAPMAN
&. HALL/CRC TAYLOR F» FRANCIS CROUP BOCA RATON LONDON NEW YORK CHAPMAN &
HALL/CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA
BUSINESS CONTENTS 1 INTRODUCTION XVII 1 MARKOV SEMIGROUPS IN W N 1 2 THE
ELLIPTIC EQUATION AND THE CAUCHY PROBLEM IN CB(M. N ): THE UNIFORMLY
ELLIPTIC CASE 3 2.0 INTRODUCTION 3 2.1 THE ELLIPTIC EQUATION AND THE
RESOLVENT R(X) 7 2.2 THE CAUCHY PROBLEM AND THE SEMIGROUP 10 2.3 THE
WEAK GENERATOR OF T(T) 21 2.4 THE MARKOV PROCESS 27 2.5 THE ASSOCIATED
STOCHASTIC DIFFERENTIAL EQUATION 30 3 ONE-DIMENSIONAL THEORY 33 3.0
INTRODUCTION 33 3.1 THE HOMOGENEOUS EQUATION 34 3.2 THE NONHOMOGENEOUS
EQUATION 41 4 UNIQUENESS RESULTS, CONSERVATION OF PROBABILITY AND MAXI-
MUM PRINCIPLES 51 4.0 INTRODUCTION 51 4.1 CONSERVATION OF PROBABILITY
AND UNIQUENESS 53 4.1.1 MAXIMUM PRINCIPLES 55 4.1.2 THE CASE WHEN C = 0
62 4.2 NONUNIQUENESS 65 5 PROPERTIES OF {T(T)} IN SPACES OF CONTINUOUS
FUNCTIONS 67 5.0 INTRODUCTION 67 5.1 COMPACTNESS OF {T(T)} 68 5.1.1 THE
CONSERVATIVE CASE 69 5.1.2 THE NONCONSERVATIVE CASE 83 5.2 ON THE
INCLUSION T{T){C B (R N )) C C 0 (R N ) 85 5.3 INVARIANCEOF C 0 (R N )
91 6 UNIFORM ESTIMATES FOR THE DERIVATIVES OF T(T)F 95 6.0 INTRODUCTION
95 6.1 UNIFORM ESTIMATES 96 VLLL 6.2 SOME CONSEQUENCES 113 7 POINTWISE
ESTIMATES FOR THE DERIVATIVES OF T(T)F 123 7.0 INTRODUCTION 123 7.1 THE
FIRST TYPE OF POINTWISE GRADIENT ESTIMATES 124 7.2 THE SECOND TYPE OF
POINTWISE GRADIENT ESTIMATES 136 7.3 FURTHER ESTIMATES IOR A = A + Y^J =
IBJ(X)DJ 150 8 INVARIANT MEASURES /I AN D THE SEMIGROUP IN L P (R N ,/I)
155 8.0 INTRODUCTION 155 8.1 EXISTENCE, UNIQUENESS AND GENERAL
PROPERTIES 158 8.1.1 GENERAL PROPERTIES AND UNIQUENESS OF THE INVARIANT
MEA- SURE OF {T(T)} 158 8.1.2 EXISTENCE BY KHAS'MINSKII THEOREM 168
8.1.3 EXISTENCE BY COMPACTNESS IN CB(R N ) 175 8.1.4 EXISTENCE BY
SYMMETRY 180 8.2 REGULARITY PROPERTIES OF INVARIANT MEASURES 185 8.2.1
GLOBAL ^-REGULARITY OF THE DENSITY P 191 8.2.2 GLOBAL SOBOLEV REGULARITY
198 8.3 SOME CONSEQUENCES OF THE ESTIMATES OF CHAPTER 6 207 8.4 THE
CONVEX CASE 211 8.5 COMPACTNESS OF T(T) AND OF THE EMBEDDING W^ P C L^
. 214 8.6 THE POINCARE INEQUALITY AND THE SPECTRAL GAP 218 8.7 THE
LOGARITHMIC SOBOLEV INEQUALITY AND HYPERCONTRACTIVITY . 221 9 THE
ORNSTEIN-UHLENBECK OPERATOR 233 9.0 INTRODUCTION 233 9.1 THE FORMULA FOR
T(T)F 235 9.2 PROPERTIES OF {T(T)} IN C B (R N ) 238 9.3 THE INVARIANT
MEASURE /I AN D THE SEMIGROUP IN L^ 243 9.3.1 THE DOMAIN OF THE
REALIZATION OF {T(T)} IN L^R 1 *) . . 254 9.3.2 THE SPECTRUM OF THE
ORNSTEIN-UHLENBECK OPERATOR IN L 264 9.3.3 THE SECTOR OF ANALYTICITY OF
THE ORNSTEIN-UHLENBECK OP- ERATOR IN L 274 9.3.4 HERMITE POLYNOMIALS
276 9.4 THE ORNSTEIN-UHLENBECK OPERATOR IN L P (R N ) 279 10 A CLASS OF
NONANALYTIC MARKOV SEMIGROUPS IN C(,(1 N ) AND IN L"(R N ,IJ.) 283 10.0
INTRODUCTION 283 10.1 NONANALYTIC SEMIGROUPS IN CB{R N ) 283 10.2
NONANALYTIC SEMIGROUPS IN L P (R N ,FI) 291 11 MARKOV SEMIGROUPS IN
UNBOUNDED OPEN SETS 297 11 THE CAUCHY-DIRICHLET PROBLEM 299 11.0
INTRODUCTION 299 11.1 TWO MAXIMUM PRINCIPLES 301 11.2 EXISTENCE AND
UNIQUENESS OF THE CLASSICAL SOLUTION 305 11.3 GRADIENT ESTIMATES 308
11.3.1 A PRIORI GRADIENT ESTIMATES 309 11.3.2 AN AUXILIARY PROBLEM 315
11.3.3 PROOF OF THEOREM 11.3.4 324 11.3.4 A COUNTEREXAMPLE TO THE
GRADIENT ESTIMATES 325 12 THE CAUCHY-NEUMANN PROBLEM: THE CONVEX CASE
329 12.0 INTRODUCTION 329 12.1 CONSTRUCTION OF THE SEMIGROUP AND UNIFORM
GRADIENT ESTIMATES 332 12.2 SOME CONSEQUENCES OF THE UNIFORM GRADIENT
ESTIMATES . 344 12.3 POINTWISE GRADIENT ESTIMATES AND THEIR
CONSEQUENCES 349 12.4 THE INVARIANT MEASURE OF THE SEMIGROUP 357 13 THE
CAUCHY-NEUMANN PROBLEM: THE NONCONVEX CASE 367 13.0 INTRODUCTION 367
13.1 THE CASE OF BOUNDED DIFFUSION COEFFICIENTS 369 13.1.1 A PRIORI
ESTIMATE 371 13.1.2 EXISTENCE OF THE SOLUTION TO PROBLEM (13.0.2) AND
UNI- FORM GRADIENT ESTIMATES 375 13.2 THE CASE WHEN FT IS AN EXTERIOR
DOMAIN 388 13.3 POINTWISE GRADIENT ESTIMATES AND THEIR CONSEQUENCES 394
13.4 THE INVARIANT MEASURE OF THE SEMIGROUP 402 13.5 FINAL REMARKS 404
III A CLASS OF MARKOV SEMIGROUPS IN R ASSOCIATED WITH DEGENERATE
ELLIPTIC OPERATORS 405 14 THE CAUCHY PROBLEM IN C B (R N ) 407 14.0
INTRODUCTION 407 14.1 SOME PRELIMINARY RESULTS ON THE OPERATOR A 409
14.2 EXISTENCE, UNIQUENESS RESULTS AND UNIFORM ESTIMATES 415 14.2.1 SOME
PRELIMINARY LEMMATA 416 14.2.2 UNIFORM ESTIMATES FOR THE SPACE
DERIVATIVES OF THE AP- PROXIMATING SEMIGROUPS {T E (T)} 419 14.2.3
CONSTRUCTION OF THE SEMIGROUP 431 14.3 SOME REMARKABLE PROPERTIES OF THE
SEMIGROUP 439 14.4 THE NONHOMOGENEOUS ELLIPTIC EQUATION 444 IV
APPENDICES 465 A BASIC NOTIONS OF FUNCTIONAL ANALYSIS IN BANACH SPACES
467 A.I BOUNDED, COMPACT AND CLOSED LINEAR OPERATORS 467 A.2 VECTOR
VALUED RIEMANN INTEGRAL 468 A.3 SPECTRUM AND RESOLVENT 470 A.4 SOME
RESULTS FROM INTERPOLATION THEORY 473 B AN OVERVIEW ON STRONGLY
CONTINUOUS AND ANALYTIC SEMIGROUPS 477 B.I STRONGLY CONTINUOUS
SEMIGROUPS 477 B.I.I ON THE CLOSURE OF THE SUM OF GENERATORS OF STRONGLY
CON- TINUOUS SEMIGROUPS 480 B.2 ANALYTIC SEMIGROUPS 482 C PDE'S AND
ANALYTIC SEMIGROUPS 487 C.I A PRIORI ESTIMATES 487 C.2 CLASSICAL MAXIMUM
PRINCIPLES 494 C.3 EXISTENCE OF CLASSICAL SOLUTION TO PDE'S AND ANALYTIC
SEMI- GROUPS 495 D SOME PROPERTIES OF THE DISTANCE FUNCTION 501 E
FUNCTION SPACES: DEFINITIONS AND MAIN PROPERTIES 505 E.I SPACES OF
FUNCTIONS THAT ARE CONTINUOUS OR HOLDER CONTINUOUS IN DOMAINS QCL" 505
E.I.I ISOTROPIC SPACES 505 E.I.2 ANISOTROPIC HOLDER SPACES IN R N 506
E.2 PARABOLIC HOLDER SPACES 508 E.3 L P AND SOBOLEV SPACES 509
REFERENCES 511 INDEX 523 |
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| author | Lorenzi, Luca Bertoldi, Marcello |
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| bvnumber | BV022885713 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV022885713 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:51:54Z |
| indexdate | 2024-07-09T21:07:44Z |
| institution | BVB |
| isbn | 1584886595 9781584886594 |
| language | English |
| lccn | 2006045837 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016090623 |
| oclc_num | 70122588 |
| open_access_boolean | |
| owner | DE-703 DE-824 |
| owner_facet | DE-703 DE-824 |
| physical | XXXI, 526 S. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Lorenzi, Luca Verfasser (DE-588)17394048X aut Analytical methods for Markov semigroups Luca Lorenzi ; Marcello Bertoldi Boca Raton [u.a.] Chapman & Hall/CRC 2007 XXXI, 526 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 283 Includes bibliographical references (p. 511-522) and index Markov, Processus de Semi-groupes Markov processes Semigroups Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 s Halbgruppe (DE-588)4022990-7 s DE-604 Bertoldi, Marcello Verfasser aut Pure and applied mathematics 283 (DE-604)BV000001885 283 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016090623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lorenzi, Luca Bertoldi, Marcello Analytical methods for Markov semigroups Pure and applied mathematics Markov, Processus de Semi-groupes Markov processes Semigroups Markov-Prozess (DE-588)4134948-9 gnd Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4134948-9 (DE-588)4022990-7 |
| title | Analytical methods for Markov semigroups |
| title_auth | Analytical methods for Markov semigroups |
| title_exact_search | Analytical methods for Markov semigroups |
| title_exact_search_txtP | Analytical methods for Markov semigroups |
| title_full | Analytical methods for Markov semigroups Luca Lorenzi ; Marcello Bertoldi |
| title_fullStr | Analytical methods for Markov semigroups Luca Lorenzi ; Marcello Bertoldi |
| title_full_unstemmed | Analytical methods for Markov semigroups Luca Lorenzi ; Marcello Bertoldi |
| title_short | Analytical methods for Markov semigroups |
| title_sort | analytical methods for markov semigroups |
| topic | Markov, Processus de Semi-groupes Markov processes Semigroups Markov-Prozess (DE-588)4134948-9 gnd Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Markov, Processus de Semi-groupes Markov processes Semigroups Markov-Prozess Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016090623&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT lorenziluca analyticalmethodsformarkovsemigroups AT bertoldimarcello analyticalmethodsformarkovsemigroups |