Physics of stochastic processes: how randomness acts in time
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
WILEY-VCH
2009
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| Edition: | 1. Aufl. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 430 S. graph. Darst. |
| ISBN: | 9783527408405 |
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| 245 | 1 | 0 | |a Physics of stochastic processes |b how randomness acts in time |c Reinhard Mahnke ; Jevgenijs Kaupuzs ; Ihor Lubashevsky |
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| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2009 | |
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| adam_text |
REINHARD MAHNKEJEVGENIJS KAUPUZS, AND IHOR LUBASHEVSKY PHYSICS OF
STOCHASTIC PROCESSES HOW RANDOMNESS ACTS IN TIME WILEY- VCH WILEY-VCH
VERLAG GMBH & CO. KGAA CONTENTS PREFACE XI PART I BASIC MATHEMATICAL
DESCRIPTION 1 1 FUNDAMENTAL CONCEPTS 3 1.1 WIENER PROCESS, ADAPTED
PROCESSES AND QUADRATIC VARIATION 3 1.2 THE SPACE OF SQUARE INTEGRABLE
RANDOM VARIABLES 8 1.3 THE ITO INTEGRAL AND THE ITO FORMULA 15 1.4 THE
KOLMOGOROV DIFFERENTIAL EQUATION AND THE FOKKER-PLANCK EQUATION 23 1.5
SPECIAL DIFFUSION PROCESSES 27 1.6 EXERCISES 29 2 MULTIDIMENSIONAL
APPROACH 31 2.1 BOUNDED MULTIDIMENSIONAL REGION 31 2.2 FROM
CHAPMAN-KOLMOGOROV EQUATION TO FOKKER-PLANCK DESCRIPTION 33 2.2.1 THE
BACKWARD FOKKER-PLANCK EQUATION 35 2.2.2 BOUNDARY SINGULARITIES 37 2.2.3
THE FORWARD FOKKER-PLANCK EQUATION 40 2.2.4 BOUNDARY RELATIONS 43 2.3
DIFFERENT TYPES OF BOUNDARIES 44 2.4 EQUIVALENT LATTICE REPRESENTATION
OF RANDOM WALKS NEAR THE BOUNDARY 45 2.4.1 DIFFUSION TENSOR
REPRESENTATIONS 46 2.4.2 EQUIVALENT LATTICE RANDOM WALKS 54 2.4.3
PROPERTIES OF THE BOUNDARY LAYER 56 2.5 EXPRESSION FOR BOUNDARY
SINGULARITIES 5$ PHYSICS OF STOCHASTIC PROCESSES: HOW RANDOMNESS ACTS IN
TIME REINHARD MAHNKE, JEVGENIJS KAUPUZS AND IHOR LUBASHEVSKY COPYRIGHT
2009 WILEY-VCH VERLAG GMBH & CO. KGAA, WEINHEIM ISBN: 978-3-527-40840-5
VI CONTENTS 2.6 DERIVATION OF SINGULAR BOUNDARY SCALING PROPERTIES 61
2.6.1 MOMENTS OF THE WALKER DISTRIBUTION AND THE GENERATING FUNCTION 61
2.6.2 MASTER EQUATION FOR LATTICE RANDOM WALKS AND ITS GENERAL SOLUTION
62 2.6.3 LIMIT OF MULTIPLE-STEP RANDOM WALKS ON SMALL TIME SCALES 65
2.6.4 CONTINUUM LIMIT AND A BOUNDARY MODEL 68 2.7 BOUNDARY CONDITION FOR
THE BACKWARD FOKKER-PLANCK EQUATION 69 2.8 BOUNDARY CONDITION FOR THE
FORWARD FOKKER-PLANCK EQUATION 71 2.9 CONCLUDING REMARKS 72 2.10
EXERCISES 73 PART 11 PHYSICS OF STOCHASTIC PROCESSES 75 3 THE MASTER
EQUATION 77 3.1 MARKOVIAN STOCHASTIC PROCESSES 77 3.2 THE MASTER
EQUATION 82 3.3 ONE-STEP PROCESSES IN FINITE SYSTEMS 85 3.4 THE
FIRST-PASSAGE TIME PROBLEM 88 3.5 THE POISSON PROCESS IN CLOSED AND OPEN
SYSTEMS 92 3.6 THE TWO-LEVEL SYSTEM 99 3.7 THE THREE-LEVEL SYSTEM 105
3.8 EXERCISES 114 4 THE FOKKER-PLANCK EQUATION 117 4.1 GENERAL
FOKKER-PLANCK EQUATIONS 117 4.2 BOUNDED DRIFT-DIFFUSION IN ONE DIMENSION
119 4.3 THE ESCAPE PROBLEM AND ITS SOLUTION 123 4.4 DERIVATION OF THE
FOKKER-PLANCK EQUATION 127 4.5 FOKKER-PLANCK DYNAMICS IN FINITE STATE
SPACE 128 4.6 FOKKER-PLANCK DYNAMICS WITH COORDINATE-DEPENDENT DIFFUSION
COEFFICIENT 133 4.7 ALTERNATIVE METHOD OF SOLVING THE FOKKER-PLANCK
EQUATION 140 4.8 EXERCISES 142 5 THE LANGEVIN EQUATION 145 5.1 A SYSTEM
OF MANY BROWNIAN PARTICLES 145 5.2 A TRADITIONAL VIEW OF THE LANGEVIN
EQUATION 251 5.3 ADDITIVE WHITE NOISE 152 , 5.4 SPECTRAL ANALYSIS 157
5.5 BROWNIAN MOTION IN THREE-DIMENSIONAL VELOCITY SPACE 160 CONTENTS VII
5.6 STOCHASTIC DIFFERENTIAL EQUATIONS 266 5.7 THE STANDARD WIENER
PROCESS 168 5.8 ARITHMETIC BROWNIAN MOTION 173 5.9 GEOMETRIC BROWNIAN
MOTION 173 5.10 EXERCISES 176 PART III APPLICATIONS 179 6
ONE-DIMENSIONAL DIFFUSION 181 6.1 RANDOM WALK ON A LINE AND DIFFUSION:
MAIN RESULTS 181 6.2 A DRUNKEN SAILOR AS RANDOM WALKER 184 6.3 DIFFUSION
WITH NATURAL BOUNDARIES 186 6.4 DIFFUSION IN A FINITE INTERVAL WITH
MIXED BOUNDARIES 193 6.5 THE MIRROR METHOD AND TIME LAG 200 6.6 MAXIMUM
VALUE DISTRIBUTION 205 6.7 SUMMARY OF RESULTS FOR DIFFUSION IN A FINITE
INTERVAL 208 6.7.1 REFLECTED DIFFUSION 208 6.7.2 DIFFUSION IN A
SEMI-OPEN SYSTEM 209 6.7.3 DIFFUSION IN AN OPEN SYSTEM 210 6.8 EXERCISES
211 7 BOUNDED DRIFT-DIFFUSION MOTION 213 7.1 DRIFT-DIFFUSION EQUATION
WITH NATURAL BOUNDARIES 213 7.2 DRIFT-DIFFUSION PROBLEM WITH ABSORBING
AND REFLECTING BOUNDARIES 215 7.3 DIMENSIONLESS DRIFT-DIFFUSION EQUATION
216 7.4 SOLUTION IN TERMS OF ORTHOGONAL EIGENFUNCTIONS 217 7.5
FIRST-PASSAGE TIME PROBABILITY DENSITY 226 7.6 CUMULATIVE BREAKDOWN
PROBABILITY 228 7.7 THE LIMITING CASE FOR LARGE POSITIVE VALUES OF THE
CONTROL PARAMETER 229 7.8 A BRIEF SURVEY OF THE EXACT SOLUTION 232 7.8.1
PROBABILITY DENSITY 233 7.8.2 OUTFLOW PROBABILITY DENSITY 234 7.8.3
FIRST MOMENT OF THE OUTFLOW PROBABILITY DENSITY 234 7.8.4 SECOND MOMENT
OF THE OUTFLOW PROBABILITY DENSITY 235 7.8.5 OUTFLOW PROBABILITY 236 7.9
RELATIONSHIP TO THE STURM-LIOUVILLE THEORY 238 7.10 ALTERNATIVE METHOD
BY THE BACKWARD FOKKER-PLANCK EQUATION 240 7.11 ROOTS OF THE
TRANSCENDENTAL EQUATION 24) 7.12 EXERCISES 251 VIII CONTENTS 8 THE
ORNSTEIN-UHLENBECK PROCESS 253 8.1 DEFINITIONS AND PROPERTIES 253 8.2
THE ORNSTEIN-UHLENBECK PROCESS AND ITS SOLUTION 254 8.3 THE
ORNSTEIN-UHLENBECK PROCESS WITH LINEAR POTENTIAL 261 8.4 THE EXPONENTIAL
ORNSTEIN-UHLENBECK PROCESS 266 8.5 OUTLOOK ON ECONOPHYSICS 268 8.6
EXERCISES 272 9 NUCLEATION IN SUPERSATURATED VAPORS 275 9.1 DYNAMICS OF
FIRST-ORDER PHASE TRANSITIONS IN FINITE SYSTEMS 275 9.2 CONDENSATION OF
SUPERSATURATED VAPOR 277 9.3 THE GENERAL MULTI-DROPLET SCENARIO 286 9.4
DETAILED BALANCE AND FREE ENERGY 290 9.5 RELAXATION TO THE FREE ENERGY
MINIMUM 294 9.6 CHEMICAL POTENTIALS 295 9.7 EXERCISES 296 10 VEHICULAR
TRAFFIC 299 10.1 THE CAR-FOLLOWING THEORY 299 10.2 THE OPTIMAL VELOCITY
MODEL AND ITS LANGEVIN APPROACH 302 10.3 TRAFFIC JAM FORMATION ON A
CIRCULAR ROAD 316 10.4 METASTABILITY NEAR PHASE TRANSITIONS IN TRAFFIC
FLOW 328 10.5 CAR CLUSTER FORMATION AS FIRST-ORDER PHASE TRANSITION 332
10.6 THERMODYNAMICS OF TRAFFIC FLOW 338 10.7 EXERCISES 348 11
NOISE-INDUCED PHASE TRANSITIONS 351 11.1 EQUILIBRIUM AND NONEQUILIBRIUM
PHASE TRANSITIONS 351 11.2 TYPES OF STOCHASTIC DIFFERENTIAL EQUATIONS
354 11.3 TRANSFORMATION OF RANDOM VARIABLES 358 11.4 FORMS OF THE
FOKKER-PLANCK EQUATION 360 11.5 THE VERHULST MODEL OF THIRD ORDER 361
11.6 THE GENETIC MODEL 364 11.7 NOISE-INDUCED INSTABILITY IN GEOMETRIC
BROWNIAN MOTION 364 11.8 SYSTEM DYNAMICS WITH STAGNATION 367 11.9
OSCILLATOR WITH DYNAMICAL TRAPS 369 ^ 11.10 DYNAMICS WITH TRAPS IN A
CHAIN OF OSCILLATORS 372 11.11 SELF-FREEZING MODEL FOR MULTI-LANE
TRAFFIC 381 11.12 EXERCISES 385 CONTENTS IX 12 MANY-PARTICLE SYSTEMS 387
12.1 HOPPING MODELS WITH ZERO-RANGE INTERACTION 387 12.2 THE ZERO-RANGE
MODEL OF TRAFFIC FLOW 389 12.3 TRANSITION RATES AND PHASE SEPARATION 392
12.4 METASTABILITY 395 12.5 MONTE CARLO SIMULATIONS OF THE HOPPING MODEL
400 12.6 FUNDAMENTAL DIAGRAM OF THE ZERO-RANGE MODEL 403 12.7
POLARIZATION KINETICS IN FERROELECTRICS WITH FLUCTUATIONS 405 12.8
EXERCISES 409 EPILOGUE 411 REFERENCES 423 INDEX 423 |
| adam_txt |
REINHARD MAHNKEJEVGENIJS KAUPUZS, AND IHOR LUBASHEVSKY PHYSICS OF
STOCHASTIC PROCESSES HOW RANDOMNESS ACTS IN TIME WILEY- VCH WILEY-VCH
VERLAG GMBH & CO. KGAA CONTENTS PREFACE XI PART I BASIC MATHEMATICAL
DESCRIPTION 1 1 FUNDAMENTAL CONCEPTS 3 1.1 WIENER PROCESS, ADAPTED
PROCESSES AND QUADRATIC VARIATION 3 1.2 THE SPACE OF SQUARE INTEGRABLE
RANDOM VARIABLES 8 1.3 THE ITO INTEGRAL AND THE ITO FORMULA 15 1.4 THE
KOLMOGOROV DIFFERENTIAL EQUATION AND THE FOKKER-PLANCK EQUATION 23 1.5
SPECIAL DIFFUSION PROCESSES 27 1.6 EXERCISES 29 2 MULTIDIMENSIONAL
APPROACH 31 2.1 BOUNDED MULTIDIMENSIONAL REGION 31 2.2 FROM
CHAPMAN-KOLMOGOROV EQUATION TO FOKKER-PLANCK DESCRIPTION 33 2.2.1 THE
BACKWARD FOKKER-PLANCK EQUATION 35 2.2.2 BOUNDARY SINGULARITIES 37 2.2.3
THE FORWARD FOKKER-PLANCK EQUATION 40 2.2.4 BOUNDARY RELATIONS 43 2.3
DIFFERENT TYPES OF BOUNDARIES 44 2.4 EQUIVALENT LATTICE REPRESENTATION
OF RANDOM WALKS NEAR THE BOUNDARY 45 2.4.1 DIFFUSION TENSOR
REPRESENTATIONS 46 2.4.2 EQUIVALENT LATTICE RANDOM WALKS 54 2.4.3
PROPERTIES OF THE BOUNDARY LAYER 56 2.5 EXPRESSION FOR BOUNDARY
SINGULARITIES 5$ PHYSICS OF STOCHASTIC PROCESSES: HOW RANDOMNESS ACTS IN
TIME REINHARD MAHNKE, JEVGENIJS KAUPUZS AND IHOR LUBASHEVSKY COPYRIGHT
2009 WILEY-VCH VERLAG GMBH & CO. KGAA, WEINHEIM ISBN: 978-3-527-40840-5
VI CONTENTS 2.6 DERIVATION OF SINGULAR BOUNDARY SCALING PROPERTIES 61
2.6.1 MOMENTS OF THE WALKER DISTRIBUTION AND THE GENERATING FUNCTION 61
2.6.2 MASTER EQUATION FOR LATTICE RANDOM WALKS AND ITS GENERAL SOLUTION
62 2.6.3 LIMIT OF MULTIPLE-STEP RANDOM WALKS ON SMALL TIME SCALES 65
2.6.4 CONTINUUM LIMIT AND A BOUNDARY MODEL 68 2.7 BOUNDARY CONDITION FOR
THE BACKWARD FOKKER-PLANCK EQUATION 69 2.8 BOUNDARY CONDITION FOR THE
FORWARD FOKKER-PLANCK EQUATION 71 2.9 CONCLUDING REMARKS 72 2.10
EXERCISES 73 PART 11 PHYSICS OF STOCHASTIC PROCESSES 75 3 THE MASTER
EQUATION 77 3.1 MARKOVIAN STOCHASTIC PROCESSES 77 3.2 THE MASTER
EQUATION 82 3.3 ONE-STEP PROCESSES IN FINITE SYSTEMS 85 3.4 THE
FIRST-PASSAGE TIME PROBLEM 88 3.5 THE POISSON PROCESS IN CLOSED AND OPEN
SYSTEMS 92 3.6 THE TWO-LEVEL SYSTEM 99 3.7 THE THREE-LEVEL SYSTEM 105
3.8 EXERCISES 114 4 THE FOKKER-PLANCK EQUATION 117 4.1 GENERAL
FOKKER-PLANCK EQUATIONS 117 4.2 BOUNDED DRIFT-DIFFUSION IN ONE DIMENSION
119 4.3 THE ESCAPE PROBLEM AND ITS SOLUTION 123 4.4 DERIVATION OF THE
FOKKER-PLANCK EQUATION 127 4.5 FOKKER-PLANCK DYNAMICS IN FINITE STATE
SPACE 128 4.6 FOKKER-PLANCK DYNAMICS WITH COORDINATE-DEPENDENT DIFFUSION
COEFFICIENT 133 4.7 ALTERNATIVE METHOD OF SOLVING THE FOKKER-PLANCK
EQUATION 140 4.8 EXERCISES 142 5 THE LANGEVIN EQUATION 145 5.1 A SYSTEM
OF MANY BROWNIAN PARTICLES 145 5.2 A TRADITIONAL VIEW OF THE LANGEVIN
EQUATION 251 5.3 ADDITIVE WHITE NOISE 152 , 5.4 SPECTRAL ANALYSIS 157
5.5 BROWNIAN MOTION IN THREE-DIMENSIONAL VELOCITY SPACE 160 CONTENTS VII
5.6 STOCHASTIC DIFFERENTIAL EQUATIONS 266 5.7 THE STANDARD WIENER
PROCESS 168 5.8 ARITHMETIC BROWNIAN MOTION 173 5.9 GEOMETRIC BROWNIAN
MOTION 173 5.10 EXERCISES 176 PART III APPLICATIONS 179 6
ONE-DIMENSIONAL DIFFUSION 181 6.1 RANDOM WALK ON A LINE AND DIFFUSION:
MAIN RESULTS 181 6.2 A DRUNKEN SAILOR AS RANDOM WALKER 184 6.3 DIFFUSION
WITH NATURAL BOUNDARIES 186 6.4 DIFFUSION IN A FINITE INTERVAL WITH
MIXED BOUNDARIES 193 6.5 THE MIRROR METHOD AND TIME LAG 200 6.6 MAXIMUM
VALUE DISTRIBUTION 205 6.7 SUMMARY OF RESULTS FOR DIFFUSION IN A FINITE
INTERVAL 208 6.7.1 REFLECTED DIFFUSION 208 6.7.2 DIFFUSION IN A
SEMI-OPEN SYSTEM 209 6.7.3 DIFFUSION IN AN OPEN SYSTEM 210 6.8 EXERCISES
211 7 BOUNDED DRIFT-DIFFUSION MOTION 213 7.1 DRIFT-DIFFUSION EQUATION
WITH NATURAL BOUNDARIES 213 7.2 DRIFT-DIFFUSION PROBLEM WITH ABSORBING
AND REFLECTING BOUNDARIES 215 7.3 DIMENSIONLESS DRIFT-DIFFUSION EQUATION
216 7.4 SOLUTION IN TERMS OF ORTHOGONAL EIGENFUNCTIONS 217 7.5
FIRST-PASSAGE TIME PROBABILITY DENSITY 226 7.6 CUMULATIVE BREAKDOWN
PROBABILITY 228 7.7 THE LIMITING CASE FOR LARGE POSITIVE VALUES OF THE
CONTROL PARAMETER 229 7.8 A BRIEF SURVEY OF THE EXACT SOLUTION 232 7.8.1
PROBABILITY DENSITY 233 7.8.2 OUTFLOW PROBABILITY DENSITY 234 7.8.3
FIRST MOMENT OF THE OUTFLOW PROBABILITY DENSITY 234 7.8.4 SECOND MOMENT
OF THE OUTFLOW PROBABILITY DENSITY 235 7.8.5 OUTFLOW PROBABILITY 236 7.9
RELATIONSHIP TO THE STURM-LIOUVILLE THEORY 238 7.10 ALTERNATIVE METHOD
BY THE BACKWARD FOKKER-PLANCK EQUATION 240 7.11 ROOTS OF THE
TRANSCENDENTAL EQUATION 24) 7.12 EXERCISES 251 VIII CONTENTS 8 THE
ORNSTEIN-UHLENBECK PROCESS 253 8.1 DEFINITIONS AND PROPERTIES 253 8.2
THE ORNSTEIN-UHLENBECK PROCESS AND ITS SOLUTION 254 8.3 THE
ORNSTEIN-UHLENBECK PROCESS WITH LINEAR POTENTIAL 261 8.4 THE EXPONENTIAL
ORNSTEIN-UHLENBECK PROCESS 266 8.5 OUTLOOK ON ECONOPHYSICS 268 8.6
EXERCISES 272 9 NUCLEATION IN SUPERSATURATED VAPORS 275 9.1 DYNAMICS OF
FIRST-ORDER PHASE TRANSITIONS IN FINITE SYSTEMS 275 9.2 CONDENSATION OF
SUPERSATURATED VAPOR 277 9.3 THE GENERAL MULTI-DROPLET SCENARIO 286 9.4
DETAILED BALANCE AND FREE ENERGY 290 9.5 RELAXATION TO THE FREE ENERGY
MINIMUM 294 9.6 CHEMICAL POTENTIALS 295 9.7 EXERCISES 296 10 VEHICULAR
TRAFFIC 299 10.1 THE CAR-FOLLOWING THEORY 299 10.2 THE OPTIMAL VELOCITY
MODEL AND ITS LANGEVIN APPROACH 302 10.3 TRAFFIC JAM FORMATION ON A
CIRCULAR ROAD 316 10.4 METASTABILITY NEAR PHASE TRANSITIONS IN TRAFFIC
FLOW 328 10.5 CAR CLUSTER FORMATION AS FIRST-ORDER PHASE TRANSITION 332
10.6 THERMODYNAMICS OF TRAFFIC FLOW 338 10.7 EXERCISES 348 11
NOISE-INDUCED PHASE TRANSITIONS 351 11.1 EQUILIBRIUM AND NONEQUILIBRIUM
PHASE TRANSITIONS 351 11.2 TYPES OF STOCHASTIC DIFFERENTIAL EQUATIONS
354 11.3 TRANSFORMATION OF RANDOM VARIABLES 358 11.4 FORMS OF THE
FOKKER-PLANCK EQUATION 360 11.5 THE VERHULST MODEL OF THIRD ORDER 361
11.6 THE GENETIC MODEL 364 11.7 NOISE-INDUCED INSTABILITY IN GEOMETRIC
BROWNIAN MOTION 364 11.8 SYSTEM DYNAMICS WITH STAGNATION 367 11.9
OSCILLATOR WITH DYNAMICAL TRAPS 369 ^ 11.10 DYNAMICS WITH TRAPS IN A
CHAIN OF OSCILLATORS 372 11.11 SELF-FREEZING MODEL FOR MULTI-LANE
TRAFFIC 381 11.12 EXERCISES 385 CONTENTS IX 12 MANY-PARTICLE SYSTEMS 387
12.1 HOPPING MODELS WITH ZERO-RANGE INTERACTION 387 12.2 THE ZERO-RANGE
MODEL OF TRAFFIC FLOW 389 12.3 TRANSITION RATES AND PHASE SEPARATION 392
12.4 METASTABILITY 395 12.5 MONTE CARLO SIMULATIONS OF THE HOPPING MODEL
400 12.6 FUNDAMENTAL DIAGRAM OF THE ZERO-RANGE MODEL 403 12.7
POLARIZATION KINETICS IN FERROELECTRICS WITH FLUCTUATIONS 405 12.8
EXERCISES 409 EPILOGUE 411 REFERENCES 423 INDEX 423 |
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| author | Mahnke, Reinhard 1952- Kaupužs, Jevgenijs Lubaševskij, Igor' A. |
| author_GND | (DE-588)135663741 |
| author_facet | Mahnke, Reinhard 1952- Kaupužs, Jevgenijs Lubaševskij, Igor' A. |
| author_role | aut aut aut |
| author_sort | Mahnke, Reinhard 1952- |
| author_variant | r m rm j k jk i a l ia ial |
| building | Verbundindex |
| bvnumber | BV035072493 |
| classification_rvk | SK 820 UG 3100 UG 3900 |
| classification_tum | PHY 015f |
| ctrlnum | (OCoLC)890591957 (DE-599)DNB988812703 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 1. Aufl. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035072493 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:04:38Z |
| indexdate | 2024-07-20T09:51:09Z |
| institution | BVB |
| isbn | 9783527408405 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016740858 |
| oclc_num | 890591957 |
| open_access_boolean | |
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| owner_facet | DE-29T DE-19 DE-BY-UBM DE-703 DE-20 DE-634 DE-11 DE-91G DE-BY-TUM |
| physical | XVII, 430 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | WILEY-VCH |
| record_format | marc |
| spelling | Mahnke, Reinhard 1952- Verfasser (DE-588)135663741 aut Physics of stochastic processes how randomness acts in time Reinhard Mahnke ; Jevgenijs Kaupuzs ; Ihor Lubashevsky 1. Aufl. Weinheim WILEY-VCH 2009 XVII, 430 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physikalisches System (DE-588)4174610-7 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Physikalisches System (DE-588)4174610-7 s Kaupužs, Jevgenijs Verfasser aut Lubaševskij, Igor' A. Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3113117&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016740858&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mahnke, Reinhard 1952- Kaupužs, Jevgenijs Lubaševskij, Igor' A. Physics of stochastic processes how randomness acts in time Physikalisches System (DE-588)4174610-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4174610-7 (DE-588)4037952-8 (DE-588)4057630-9 (DE-588)4123623-3 |
| title | Physics of stochastic processes how randomness acts in time |
| title_auth | Physics of stochastic processes how randomness acts in time |
| title_exact_search | Physics of stochastic processes how randomness acts in time |
| title_exact_search_txtP | Physics of stochastic processes how randomness acts in time |
| title_full | Physics of stochastic processes how randomness acts in time Reinhard Mahnke ; Jevgenijs Kaupuzs ; Ihor Lubashevsky |
| title_fullStr | Physics of stochastic processes how randomness acts in time Reinhard Mahnke ; Jevgenijs Kaupuzs ; Ihor Lubashevsky |
| title_full_unstemmed | Physics of stochastic processes how randomness acts in time Reinhard Mahnke ; Jevgenijs Kaupuzs ; Ihor Lubashevsky |
| title_short | Physics of stochastic processes |
| title_sort | physics of stochastic processes how randomness acts in time |
| title_sub | how randomness acts in time |
| topic | Physikalisches System (DE-588)4174610-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Physikalisches System Mathematische Physik Stochastischer Prozess Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3113117&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016740858&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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