Stochastic methods: a handbook for the natural and social sciences
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Springer series in synergetics
13 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017096425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 447 S. graph. Darst. |
| ISBN: | 9783540707127 3540707123 |
Internformat
MARC
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| 100 | 1 | |a Gardiner, Crispin W. |d 1942- |e Verfasser |0 (DE-588)108947959X |4 aut | |
| 245 | 1 | 0 | |a Stochastic methods |b a handbook for the natural and social sciences |c Crispin Gardiner |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XVII, 447 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Springer series in synergetics |v 13 | |
| 490 | 0 | |a Springer complexity | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Analysis |0 (DE-588)4132272-1 |D s |
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| 689 | 0 | |5 DE-604 | |
| 787 | 0 | 8 | |i Überarbeitung von |a Gardiner, Crispin W. |t Handbook of stochastic methods for physics, chemistry and the natural sciences |
| 830 | 0 | |a Springer series in synergetics |v 13 |w (DE-604)BV000005271 |9 13 | |
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Datensatz im Suchindex
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| adam_text | CRISPIN GARDINER STOCHASTIC METHODS A HANDBOOK FOR THE NATURAL AND
SOCIAL SCIENCES FOURTH EDITION 4^ SPRINGER CONTENTS 1. A HISTORICAL
INTRODUCTION 1 1.1 MOTIVATION 1 1.2 SOME HISTORICAL EXAMPLES 2 1.2.1
BROWNIAN MOTION 2 1.2.2 LANGEVIN S EQUATION 6 1.3 THE STOCK MARKET 8
1.3.1 STATISTICS OF RETURNS 8 1.3.2 FINANCIAL DERIVATIVES 9 1.3.3 THE
BLACK-SCHOLES FORMULA 10 1.3.4 HEAVY TAILED DISTRIBUTIONS 10 1.4
BIRTH-DEATH PROCESSES 11 1.5 NOISE IN ELECTRONIC SYSTEMS 14 1.5.1 SHOT
NOISE 14 1.5.2 AUTOCORRELATION FUNCTIONS AND SPECTRA 18 1.5.3 FOURIER
ANALYSIS OF FLUCTUATING FUNCTIONS: STATIONARY SYSTEMS 19 1.5.4 JOHNSON
NOISE AND NYQUIST S THEOREM 20 2. PROBABILITY CONCEPTS 23 2.1 EVENTS,
AND SETS OF EVENTS 23 2.2 PROBABILITIES 24 2.2.1 PROBABILITY AXIOMS 24
2.2.2 THE MEANING OF P(A) 25 2.2.3 THE MEANING OF THE AXIOMS 25 2.2.4
RANDOM VARIABLES 26 2.3 JOINT AND CONDITIONAL PROBABILITIES:
INDEPENDENCE 27 2.3.1 JOINT PROBABILITIES 27 2.3.2 CONDITIONAL
PROBABILITIES 27 2.3.3 RELATIONSHIP BETWEEN JOINT PROBABILITIES OF
DIFFERENT ORDERS 28 2.3.4 INDEPENDENCE 28 2.4 MEAN VALUES AND
PROBABILITY DENSITY 29 2.4.1 DETERMINATION OF PROBABILITY DENSITY BY
MEANS OF ARBITRARY FUNCTIONS 30 2.4.2 SETS OF PROBABILITY ZERO 30 2.5
THE INTERPRETATION OF MEAN VALUES 31 2.5.1 MOMENTS, CORRELATIONS, AND
COVARIANCES 32 2.5.2 THE LAW OF LARGE NUMBERS 32 2.6 CHARACTERISTIC
FUNCTION 33 2.7 CUMULANT GENERATING FUNCTIONS CORRELATION FUNCTIONS AND
CUMULANTS 34 2.7.1 EXAMPLE: CUMULANT OF ORDER 4: ((X^X^)) 36 2.7.2
SIGNIFICANCE OF CUMULANTS 36 2.8 GAUSSIAN AND POISSONIAN PROBABILITY
DISTRIBUTIONS 37 X CONTENTS 2.8.1 THE GAUSSIAN DISTRIBUTION 37 2.8.2
CENTRAL LIMIT THEOREM 38 2.8.3 THE POISSON DISTRIBUTION 39 2.9 LIMITS OF
SEQUENCES OF RANDOM VARIABLES 40 2.9.1 ALMOST CERTAIN LIMIT 40 2.9.2
MEAN SQUARE LIMIT (LIMIT IN THE MEAN) 41 2.9.3 STOCHASTIC LIMIT, OR
LIMIT IN PROBABILITY 41 2.9.4 LIMIT IN DISTRIBUTION 41 2.9.5
RELATIONSHIP BETWEEN LIMITS 41 3. MARKOV PROCESSES 42 3.1 STOCHASTIC
PROCESSES 42 3.1.1 KINDS OF STOCHASTIC PROCESS 42 3.2 MARKOV PROCESS 43
3.2.1 CONSISTENCY*THE CHAPMAN-KOLMOGOROV EQUATION 44 3.2.2 DISCRETE
STATE SPACES 44 3.2.3 MORE GENERAL MEASURES 45 3.3 CONTINUITY IN
STOCHASTIC PROCESSES 45 3.3.1 MATHEMATICAL DEFINITION OF A CONTINUOUS
MARKOV PROCESS .. 46 3.4 DIFFERENTIAL CHAPMAN-KOLMOGOROV EQUATION 47
3.4.1 DERIVATION OF THE DIFFERENTIAL CHAPMAN-KOLMOGOROV EQUATION 48
3.4.2 STATUS OF THE DIFFERENTIAL CHAPMAN-KOLMOGOROV EQUATION .. 51 3.5
INTERPRETATION OF CONDITIONS AND RESULTS 51 3.5.1 JUMP PROCESSES: THE
MASTER EQUATION 51 3.5.2 DIFFUSION PROCESSES*THE FOKKER-PLANCK EQUATION
52 3.5.3 DETERMINISTIC PROCESSES*LIOUVILLE S EQUATION 54 3.5.4 GENERAL
PROCESSES 55 3.6 EQUATIONS FOR TIME DEVELOPMENT IN INITIAL TIME*BACKWARD
EQUATIONS 55 3.7 STATIONARY AND HOMOGENEOUS MARKOV PROCESSES 56 3.7.1
ERGODIC PROPERTIES 57 3.7.2 HOMOGENEOUS PROCESSES 60 3.7.3 APPROACH TO A
STATIONARY PROCESS 60 3.7.4 AUTOCORRELATION FUNCTION FOR MARKOV
PROCESSES 63 3.8 EXAMPLES OF MARKOV PROCESSES 65 3.8.1 THE WIENER
PROCESS 65 3.8.2 THE RANDOM WALK IN ONE DIMENSION 68 3.8.3 POISSON
PROCESS 71 3.8.4 THE ORNSTEIN-UHLENBECK PROCESS 72 3.8.5 RANDOM
TELEGRAPH PROCESS 75 CONTENTS XI 4. THE ITO CALCULUS AND STOCHASTIC
DIFFERENTIAL EQUATIONS 77 4.1 MOTIVATION 77 4.2 STOCHASTIC INTEGRATION
79 4.2.1 DEFINITION OF THE STOCHASTIC INTEGRAL 79 4.2.2 ITO STOCHASTIC
INTEGRAL 81 4.2.3 EXAMPLE J W(F)DW(F) 81 4.2.4 THE STRATONOVICH
INTEGRAL 82 4.2.5 NONANTICIPATING FUNCTIONS 82 4.2.6 PROOF THAT DW(TF =
DT AND DW(T) 2+N =0 83 4.2.7 PROPERTIES OF THE ITO STOCHASTIC INTEGRAL
85 4.3 STOCHASTIC DIFFERENTIAL EQUATIONS (SDE) 88 4.3.1 ITO STOCHASTIC
DIFFERENTIAL EQUATION: DEFINITION 89 4.3.2 DEPENDENCE ON INITIAL
CONDITIONS AND PARAMETERS 91 4.3.3 MARKOV PROPERTY OF THE SOLUTION OF AN
ITO SDE 92 4.3.4 CHANGE OF VARIABLES: ITO S FORMULA 92 4.3.5 CONNECTION
BETWEEN FOKKER-PLANCK EQUATION AND STOCHASTIC DIFFERENTIAL EQUATION 93
4.3.6 MULTIVARIABLE SYSTEMS 95 4.4 THE STRATONOVICH STOCHASTIC INTEGRAL
96 4.4.1 DEFINITION OF THE STRATONOVICH STOCHASTIC INTEGRAL 96 4.4.2
STRATONOVICH STOCHASTIC DIFFERENTIAL EQUATION 96 4.5 SOME EXAMPLES AND
SOLUTIONS 99 4.5.1 COEFFICIENTS WITHOUT X DEPENDENCE 99 4.5.2
MULTIPLICATIVE LINEAR WHITE NOISE PROCESS*GEOMETRIC BROWNIAN MOTION 100
4.5.3 COMPLEX OSCILLATOR WITH NOISY FREQUENCY 101 4.5.4
ORNSTEIN-UHLENBECK PROCESS 103 4.5.5 CONVERSION FROM CARTESIAN TO POLAR
COORDINATES 104 4.5.6 MULTIVARIATE ORNSTEIN-UHLENBECK PROCESS 105 4.5.7
THE GENERAL SINGLE VARIABLE LINEAR EQUATION 108 4.5.8 MULTIVARIABLE
LINEAR EQUATIONS , 110 4.5.9 TIME-DEPENDENT ORNSTEIN-UHLENBECK PROCESS
ILL 5. THE FOKKER-PLANCK EQUATION 113 5.1 PROBABILITY CURRENT AND
BOUNDARY CONDITIONS 114 5.1.1 CLASSIFICATION OF BOUNDARY CONDITIONS 116
5.1.2 BOUNDARY CONDITIONS FOR THE BACKWARD FOKKER- PLANCK EQUATION 116
5.2 FOKKER-PLANCK EQUATION IN ONE DIMENSION 117 5.2.1 BOUNDARY
CONDITIONS IN ONE DIMENSION 118 5.3 STATIONARY SOLUTIONS FOR HOMOGENEOUS
FOKKER-PLANCK EQUATIONS... 120 5.3.1 EXAMPLES OF STATIONARY .SOLUTIONS
122 5.4 EIGENFUNCTION METHODS FOR HOMOGENEOUS PROCESSES 124 5.4.1
EIGENFUNCTIONS FOR REFLECTING BOUNDARIES 124 5.4.2 EIGENFUNCTIONS FOR
ABSORBING BOUNDARIES 126 XII CONTENTS 5.4.3 EXAMPLES 126 5.5 FIRST
PASSAGE TIMES FOR HOMOGENEOUS PROCESSES 130 5.5.1 TWO ABSORBING BARRIERS
130 5.5.2 ONE ABSORBING BARRIER 132 5.5.3 APPLICATION*ESCAPE OVER A
POTENTIAL BARRIER 133 5.5.4 PROBABILITY OF EXIT THROUGH A PARTICULAR END
OF THE INTERVAL. 135 6. THE FOKKER-PLANCK EQUATION IN SEVERAL DIMENSIONS
138 6.1 CHANGE OF VARIABLES 138 6.2 STATIONARY SOLUTIONS OF MANY
VARIABLE FOKKER-PLANCK EQUATIONS ... 140 6.2.1 BOUNDARY CONDITIONS 140
6.2.2 POTENTIAL CONDITIONS 141 6.3 DETAILED BALANCE 142 6.3.1 DEFINITION
OF DETAILED BALANCE 142 6.3.2 DETAILED BALANCE FOR A MARKOV PROCESS 143
6.3.3 CONSEQUENCES OF DETAILED BALANCE FOR STATIONARY MEAN,
AUTOCORRELATION FUNCTION AND SPECTRUM 144 6.3.4 SITUATIONS IN WHICH
DETAILED BALANCE MUST BE GENERALISED . 144 6.3.5 IMPLEMENTATION OF
DETAILED BALANCE IN THE DIFFERENTIAL CHAPMAN-KOLMOGOROV EQUATION 145 6.4
EXAMPLES OF DETAILED BALANCE IN FOKKER-PLANCK EQUATIONS 149 6.4.1
KRAMERS EQUATION FOR BROWNIAN MOTION IN A POTENTIAL 149 6.4.2
DETERMINISTIC MOTION 152 6.4.3 DETAILED BALANCE IN MARKOVIAN PHYSICAL
SYSTEMS 153 6.4.4 ORNSTEIN-UHLENBECK PROCESS 153 6.4.5 THE ONSAGER
RELATIONS 155 6.4.6 SIGNIFICANCE OF THE ONSAGER RELATIONS*FLUCTUATION-
DISSIPATION THEOREM 156 6.5 EIGENFUNCTION METHODS IN MANY VARIABLES 158
6.5.1 RELATIONSHIP BETWEEN FORWARD AND BACKWARD EIGENFUNCTIONS 159 6.5.2
EVEN VARIABLES ONLY*NEGATIVITY OF EIGENVALUES 159 6.5.3 A VARIATIONAL
PRINCIPLE 160 6.5.4 CONDITIONAL PROBABILITY 161 6.5.5 AUTOCORRELATION
MATRIX 161 6.5.6 SPECTRUM MATRIX 162 6.6 FIRST EXIT TIME FROM A REGION
(HOMOGENEOUS PROCESSES) 163 6.6.1 SOLUTIONS OF MEAN EXIT TIME PROBLEMS
164 6.6.2 DISTRIBUTION OF EXIT POINTS 166 7. SMALL NOISE APPROXIMATIONS
FOR DIFFUSION PROCESSES 169 7.1 COMPARISON OF SMALL NOISE EXPANSIONS FOR
STOCHASTIC DIFFERENTIAL EQUATIONS AND FOKKER-PLANCK EQUATIONS 169 7.2
SMALL NOISE EXPANSIONS FOR STOCHASTIC DIFFERENTIAL EQUATIONS 171 7.2.1
VALIDITY OF THE EXPANSION 174 7.2.2 STATIONARY SOLUTIONS (HOMOGENEOUS
PROCESSES) 175 CONTENTS XIII 7.2.3 MEAN, VARIANCE, AND TIME CORRELATION
FUNCTION 175 7.2.4 FAILURE OF SMALL NOISE PERTURBATION THEORIES 176 7.3
SMALL NOISE EXPANSION OF THE FOKKER-PLANCK EQUATION 178 7.3.1 EQUATIONS
FOR MOMENTS AND AUTOCORRELATION FUNCTIONS 180 7.3.2 EXAMPLE 182 7.3.3
ASYMPTOTIC METHOD FOR STATIONARY DISTRIBUTION 184 8. THE WHITE NOISE
LIMIT 185 8.1 WHITE NOISE PROCESS AS A LIMIT OF NONWHITE PROCESS 185
8.1.1 FORMULATION OF THE LIMIT 186 8.1.2 GENERALISATIONS OF THE METHOD
189 8.2 BROWNIAN MOTION AND THE SMOLUCHOWSKI EQUATION 192 8.2.1
SYSTEMATIC FORMULATION IN TERMS OF OPERATORS AND PROJECTORS 194 8.2.2
SHORT-TIME BEHAVIOUR 195 8.2.3 BOUNDARY CONDITIONS 197 8.2.4 EVALUATION
OF HIGHER ORDER CORRECTIONS 198 8.3 ADIABATIC ELIMINATION OF FAST
VARIABLES: THE GENERAL CASE 202 8.3.1 EXAMPLE: ELIMINATION OF
SHORT-LIVED CHEMICAL INTERMEDIATES202 8.3.2 ADIABATIC ELIMINATION IN
HAKEN S MODEL 206 8.3.3 ADIABATIC ELIMINATION OF FAST VARIABLES: A
NONLINEAR CASE . 210 8.3.4 AN EXAMPLE WITH ARBITRARY NONLINEAR COUPLING
214 9. BEYOND THE WHITE NOISE LIMIT 216 9.1 SPECIFICATION OF THE PROBLEM
217 9.1.1 EIGENFUNCTIONS OF LI 218 9.1.2 PROJECTORS 218 9.2 BLOCH S
PERTURBATION THEORY 219 9.2.1 FORMALISM FOR THE PERTURBATION THEORY 220
9.2.2 APPLICATION OF BLOCH S PERTURBATION THEORY 222 9.2.3 CONSTRUCTION
OF THE CONDITIONAL PROBABILITY 223 9.2.4 STATIONARY SOLUTION P S {X, P)
226 9.2.5 EXAMPLES 226 9.2.6 GENERALISATION TO A SYSTEM DRIVEN BY
SEVERAL MARKOV PROCESSES 228 9.3 COMPUTATION OF CORRELATION FUNCTIONS
230 9.3.1 SPECIAL RESULTS FOR ORNSTEIN-UHLENBECK P(T) 232 9.3.2
GENERALISATION TO ARBITRARY GAUSSIAN INPUTS 232 9.4 THE WHITE NOISE
LIMIT 233 9.4.1 RELATION OF THE WHITE NOISE LIMIT OF (X(T);(0)) TO THE
IMPULSE RESPONSE FUNCTION 233 10. LEVY PROCESSES AND FINANCIAL
APPLICATIONS 235 10.1 STOCHASTIC DESCRIPTION OF STOCK PRICES 235 10.2
THE BROWNIAN MOTION DESCRIPTION OF FINANCIAL MARKETS 237 10.2.1
FINANCIAL ASSETS 237 XIV CONTENTS 10.2.2 LONG AND SHORT POSITIONS
238 10.2.3 PERFECT LIQUIDITY 238 10.2.4 THE BLACK-SCHOLES FORMULA 238
10.2.5 EXPLICIT SOLUTION FOR THE OPTION PRICE 240 10.2.6 ANALYSIS OF THE
FORMULA 242 10.2.7 THE RISK-NEUTRAL FORMULATION 244 10.2.8 CHANGE OF
MEASURE AND GIRSANOV S THEOREM 245 10.3 HEAVY TAILS AND LEVY PROCESSES
248 10.3.1 LEVY PROCESSES 248 10.3.2 INFINITE DIVISIBILITY 249 10.3.3
THE POISSON PROCESS 250 10.3.4 THE COMPOUND POISSON PROCESS 250 10.3.5
LEVY PROCESSES WITH INFINITE INTENSITY 251 10.3.6 THE LEVY-KHINCHIN
FORMULA 252 10.4 THE PARETIAN PROCESSES 252 10.4.1 SHAPES OF THE
PARETIAN DISTRIBUTIONS 255 10.4.2 THE EVENTS OF A PARETIAN PROCESS 255
10.4.3 STABLE PROCESSES 257 10.4.4 OTHER LEVY PROCESSES 258 10.5
MODELLING THE EMPIRICAL BEHAVIOUR OF FINANCIAL MARKETS 258 10.5.1
STYLISED STATISTICAL FACTS ON ASSET RETURNS 258 10.5.2 THE PARETIAN
PROCESS DESCRIPTION 259 10.5.3 IMPLICATIONS FOR REALISTIC MODELS 259
10.5.4 EQUIVALENT MARTINGALE MEASURE 260 10.5.5 HYPERBOLIC MODELS 262
10.5.6 CHOICE OF MODELS 262 10.6 EPILOGUE*THE CRASH OF 2008 263 11.
MASTER EQUATIONS AND JUMP PROCESSES 26 4 11.1 BIRTH-DEATH MASTER
EQUATIONS*ONE VARIABLE 264 11.1.1 STATIONARY SOLUTIONS 265 11.1.2
EXAMPLE: CHEMICAL REACTION X ^ A 267 11.1.3 A CHEMICAL BISTABLE SYSTEM
269 11.2 APPROXIMATION OF MASTER EQUATIONS BY FOKKER-PLANCK EQUATIONS ..
273 11.2.1 JUMP PROCESS APPROXIMATION OF A DIFFUSION PROCESS 273 11.2.2
THE KRAMERS-MOYAL EXPANSION 275 11.2.3 VAN KAMPEN S SYSTEM SIZE
EXPANSION 276 11.2.4 KURTZ S THEOREM 280 11.2.5 CRITICAL FLUCTUATIONS
281 11.3 BOUNDARY CONDITIONS FOR BIRTH-DEATH PROCESSES 283 11.4 MEAN
FIRST PASSAGE TIMES 284 11.4.1 PROBABILITY OF ABSORPTION I 286 11.4.2
COMPARISON WITH FOKKER-PLANCK EQUATION 286 11.5 BIRTH-DEATH SYSTEMS WITH
MANY VARIABLES 287 11.5.1 STATIONARY SOLUTIONS WHEN DETAILED BALANCE
HOLDS 288 CONTENTS XV 11.5.2 STATIONARY SOLUTIONS WITHOUT DETAILED
BALANCE (KIRCHOFF S SOLUTION) 290 11.5.3 SYSTEM SIZE EXPANSION AND
RELATED EXPANSIONS 291 11.6 SOME EXAMPLES 291 11.6.1 X + A^2X 291
11.6.2 X^Y^A 292 * R 11.6.3 PREY-PREDATOR SYSTEM 292 11.6.4 GENERATING
FUNCTION EQUATIONS 297 12. THE POISSON REPRESENTATION 301 12.1
FORMULATION OF THE POISSON REPRESENTATION 301 12.2 KINDS OF POISSON
REPRESENTATIONS 305 12.2.1 REAL POISSON REPRESENTATIONS 305 12.2.2
COMPLEX POISSON REPRESENTATIONS 306 12.2.3 THE POSITIVE POISSON
REPRESENTATION 309 12.3 TIME CORRELATION FUNCTIONS 313 12.3.1
INTERPRETATION IN TERMS OF STATISTICAL MECHANICS 314 12.3.2 LINEARISED
RESULTS 318 12.4 TRIMOLECULAR REACTION 318 12.4.1 FOKKER-PLANCK EQUATION
FOR TRIMOLECULAR REACTION 319 12.4.2 THIRD-ORDER NOISE 323 12.4.3
EXAMPLE OF THE USE OF THIRD-ORDER NOISE 324 12.5 SIMULATIONS USING THE
POSITIVE POISSON REPRESENTATION 326 12.5.1 ANALYTIC TREATMENT VIA THE
DETERMINISTIC EQUATION 326 12.5.2 FULL STOCHASTIC CASE 329 12.5.3
TESTING THE VALIDITY OF POSITIVE POISSON SIMULATIONS 331 12.6
APPLICATION OF THE POISSON REPRESENTATION TO POPULATION DYNAMICS . 332
12.6.1 THE LOGISTIC MODEL 332 12.6.2 POISSON REPRESENTATION STOCHASTIC
DIFFERENTIAL EQUATION.... 333 12.6.3 ENVIRONMENTAL NOISE 333 12.6.4
EXTINCTION 334 13. SPATIALLY DISTRIBUTED SYSTEMS 336 13.1 BACKGROUND 336
13.1.1 FUNCTIONAL FOKKER-PLANCK EQUATIONS 338 13.2 MULTIVARIATE MASTER
EQUATION DESCRIPTION 339 13.2.1 CONTINUUM FORM OF DIFFUSION MASTER
EQUATION 341 13.2.2 COMBINING REACTIONS AND DIFFUSION 345 13.2.3 POISSON
REPRESENTATION METHODS 346 13.3 SPATIAL AND TEMPORAL CORRELATION
STRUCTURES 347 13.3.1 REACTIONX^K 347 , 13.3.2 REACTIONS B + X^C, A+X*
- 2X 350 13.3.3 A NONLINEAR MODEL WITH A SECOND-ORDER PHASE TRANSITION..
355 14. 14. 14. 14. 14. LI L.2 1.3 1.4 1.5 XVI CONTENTS 13.4 CONNECTION
BETWEEN LOCAL AND GLOBAL DESCRIPTIONS 359 13.4.1 EXPLICIT ADIABATIC
ELIMINATION OF INHOMOGENEOUS MODES .. 360 13.5 PHASE-SPACE MASTER
EQUATION 362 13.5.1 TREATMENT OF FLOW 362 13.5.2 FLOW AS A BIRTH-DEATH
PROCESS 363 13.5.3 INCLUSION OF COLLISIONS*THE BOLTZMANN MASTER
EQUATION... 366 13.5.4 COLLISIONS AND FLOW TOGETHER 369 14. BISTABILITY,
METASTABILITY, AND ESCAPE PROBLEMS 372 14.1 DIFFUSION IN A DOUBLE-WELL
POTENTIAL (ONE VARIABLE) 372 BEHAVIOUR FOR D = 0 373 BEHAVIOUR IF D IS
VERY SMALL 373 EXIT TIME 375 SPLITTING PROBABILITY 375 DECAY FROM AN
UNSTABLE STATE 377 14.2 EQUILIBRATION OF POPULATIONS IN EACH WELL 378
14.2.1 KRAMERS METHOD 378 14.2.2 EXAMPLE: REVERSIBLE DENATURATION OF
CHYMOTRYPSINOGEN ... 382 14.2.3 BISTABILITY WITH BIRTH-DEATH MASTER
EQUATIONS (ONE VARIABLE) 384 14.3 BISTABILITY IN MULTIVARIABLE SYSTEMS
386 14.3.1 DISTRIBUTION OF EXIT POINTS 387 14.3.2 ASYMPTOTIC ANALYSIS OF
MEAN EXIT TIME 391 14.3.3 KRAMERS METHOD IN SEVERAL DIMENSIONS 392
14.3.4 EXAMPLE: BROWNIAN MOTION IN A DOUBLE POTENTIAL 394 15. SIMULATION
OF STOCHASTIC DIFFERENTIAL EQUATIONS 401 15.1 THE ONE VARIABLE TAYLOR
EXPANSION 402 15.1.1 EULER METHODS 402 15.1.2 HIGHER ORDERS 402 15.1.3
MULTIPLE STOCHASTIC INTEGRALS 403 15.1.4 THE EULER ALGORITHM 404 15.1.5
MILSTEIN ALGORITHM 406 15.2 THE MEANING OF WEAK AND STRONG CONVERGENCE
407 15.3 STABILITY 407 15.3.1 CONSISTENCY 410 15.4 IMPLICIT AND
SEMI-IMPLICIT ALGORITHMS 410 15.5 VECTOR STOCHASTIC DIFFERENTIAL
EQUATIONS 411 15.5.1 FORMULAE AND NOTATION 412 15.5.2 MULTIPLE
STOCHASTIC INTEGRALS 412 15.5.3 THE VECTOR EULER ALGORITHM 414 15.5.4
THE VECTOR MILSTEIN ALGORITHM 414 15.5.5 THE STRONG VECTOR SEMI-IMPLICIT
ALGORITHM 415 15.5.6 THE WEAK VECTOR SEMI-IMPLICIT ALGORITHM 415 15.6
HIGHER ORDER ALGORITHMS 416 15.7 STOCHASTIC PARTIAL DIFFERENTIAL
EQUATIONS 417 CONTENTS XVII 15.7.1 FOURIER TRANSFORM METHODS 418 15.7.2
THE INTERACTION PICTURE METHOD 419 15.8 SOFTWARE RESOURCES 420
REFERENCES 421 BIBLIOGRAPHY 429 AUTHOR INDEX 434 SYMBOL INDEX 435
SUBJECT INDEX 439
|
| any_adam_object | 1 |
| author | Gardiner, Crispin W. 1942- |
| author_GND | (DE-588)108947959X |
| author_facet | Gardiner, Crispin W. 1942- |
| author_role | aut |
| author_sort | Gardiner, Crispin W. 1942- |
| author_variant | c w g cw cwg |
| building | Verbundindex |
| bvnumber | BV035291380 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274 |
| callnumber-search | QA274 |
| callnumber-sort | QA 3274 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 QH 440 SK 820 SK 950 UG 3900 |
| classification_tum | MAT 606f PHY 015f |
| ctrlnum | (OCoLC)277069162 (DE-599)BVBBV035291380 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV035291380 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:27:49Z |
| institution | BVB |
| isbn | 9783540707127 3540707123 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017096425 |
| oclc_num | 277069162 |
| open_access_boolean | |
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| physical | XVII, 447 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in synergetics |
| series2 | Springer series in synergetics Springer complexity |
| spellingShingle | Gardiner, Crispin W. 1942- Stochastic methods a handbook for the natural and social sciences Springer series in synergetics Stochastic processes Stochastische Analysis (DE-588)4132272-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4037952-8 |
| title | Stochastic methods a handbook for the natural and social sciences |
| title_auth | Stochastic methods a handbook for the natural and social sciences |
| title_exact_search | Stochastic methods a handbook for the natural and social sciences |
| title_full | Stochastic methods a handbook for the natural and social sciences Crispin Gardiner |
| title_fullStr | Stochastic methods a handbook for the natural and social sciences Crispin Gardiner |
| title_full_unstemmed | Stochastic methods a handbook for the natural and social sciences Crispin Gardiner |
| title_short | Stochastic methods |
| title_sort | stochastic methods a handbook for the natural and social sciences |
| title_sub | a handbook for the natural and social sciences |
| topic | Stochastic processes Stochastische Analysis (DE-588)4132272-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Stochastic processes Stochastische Analysis Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017096425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005271 |
| work_keys_str_mv | AT gardinercrispinw stochasticmethodsahandbookforthenaturalandsocialsciences |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 606f 2016 A 2912(4)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Ausgeliehen – Rückgabe bis: 10.06.2025 |
Teilbibliothek Physik
| Signatur: |
0202 MAT 606f 2010 A 523(4)
Lageplan 0204 MAT 606f 2010 A 523(4) Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 1 | Nicht ausleihbar Am Standort |
Teilbibliothek Chemie, Lehrbuchsammlung
| Signatur: |
0303 MAT 606f 2017 L 266(4)
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Ausgeliehen – Rückgabe bis: 06.06.2025 |
| Exemplar 2 | Ausleihbar Ausgeliehen – Rückgabe bis: 18.06.2025 |
| Exemplar 3 | Ausleihbar Am Standort |
| Exemplar 4 | Ausleihbar Am Standort |
| Exemplar 5 | Ausleihbar Am Standort |