Kannan D. (ed.), Lakshmikantham V. (ed.) — Handbook of stochastic analysis and applications :: Электронная библиотека попечительского совета мехмата МГУ

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Kannan D. (ed.), Lakshmikantham V. (ed.) — Handbook of stochastic analysis and applications

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Название: Handbook of stochastic analysis and applications

Авторы: Kannan D. (ed.), Lakshmikantham V. (ed.)

Аннотация:

Twelve contributions from mathematicians in the U.S., Russia, China, and Israel present an overview of the analysis of some basic stochastic processes and stochastic equations as well as certain of their applications. Chapters in the first half of the text are devoted largely to theory, while the remainder focus on applications. A sampling of topics includes Markov processes, semimartingales, Hida's white noise theory, large deviations, control theory, stochastic game theory, and the application of optimization problems to financial mathematics.

Язык:

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 763

Добавлена в каталог: 04.06.2005

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Предметный указатель

Pre- $\tau$       2
Pre- $\tau$ $\sigma$ -field      3
Predictable      48 53 59 87
Predictable decomposition      100
Predictable projection      58 88
Predictable quadratic      62
Predictable representability      99 101
Predictable time      54
Predictably      87
Prelocally integrable      59
Premature convergence      645
Principle of coherence      256
Probability of extinction      8
Process      53
Process level LDP      403
Progressive      53 78
Progressively measurable processes      392
Prohorov’s theorem      376
Projection      59
Projection algorithm      582
Projections      59
Projective limit      386 403
Projective system      386
Proportional transactional costs      708
Pure      27
Pure birth process      10
Pure jump process      21
Pure jump processes      22
Purely discontinuous      54 62
Quadratic covariation      62 64 65 83
Quadratic variation      62 64 65
Quasi-left-continuous      57
Quasi-martingale      65
Quasi-potential      394
radiaL      34
Random directions      594
random intervals      53
Random map      15
Random measure      87
Random search      634
Random time-change      55
Random walk      15
Rao’s decomposition      65
Rapidly decreasing      111
Rate function      363
Rate of convergence      584 590
Recombination      658
Recurrence      29
Recurrent      4 28 34 35 440
Recurrent set      12
Recursive utilities      706
Reflecting boundary conditions      7
Reflecting diffusio      713
Reflection      27
Regular      26
Regular space      374
Rehedging      741
Relative entropy      367
Relative, risk aversion      681
Relax      738
Renormalization      114
Replicates      741
Replicating policies      725
Replicating portfolio      727
Replicating strategies      726
Replication errors      742
Resolvent operator      23
Resolvent set      23
restarting      654
retention      637
Right-closable      48
Risk functionals      738
Risk management      703
Risk-sensitive control      550 557 706
Risky investment      722
Robbins — Monro algorithm      577 579
Rockafellar’s lemma      371
Rosenbrock method: r-stage      248
Rosenbrock methods: stochastic      248
Roulette wheel selection      658
Runge — Kutta      243
Runge — Kutta methods      254
S      400 410
Sa      511
SA differential inclusion      615
SA efficiency      596
SA global      584
SA large deviations      594 595
SA parallel processing      609 616
SA robustness      616
SA saddle-point      483 512
SA sample path      52
SA stopping rule      594
Sanov’s theorem      368 399 400 409
Scale function      25
Scaling      144
Schilder’s theorem      390
SDE      33 84 160 589
SDE driven by nonlinear integrator      204
SDE governed by Levy process      194
SDE limit      593
SDE on Manifold      168
SDE with anticipating drift      221
SDE with Jump      191
SDE with respect to martingale      198
Section theorem      55
Selection      30 658
Sell      112
Selling stock      112
Semimartingale      64
Set      53
Set: hierarchical      243
Set: remainder      243
Settling point      640
SFDE      213
Share of stock      112
Shift invariance      402
Singular stochastic control      106 101
Singular trading policies      101
Skorohad problem      116
Skorohod problem      116
Small set      12
Snell envelope      51
Soft constraint      583
Solution      84
Space: Cochran — Kuo — Sengupta      122
Space: Hida — Kubo — Takenaka      119
Space: Kondratiev — Streit      120
Special semimartingale      65
Speed function      25
Speedup      638

Splitting: additive      259
Splitting: multiplicative      259
Stability      165 439
Stable      15 491
Stable equilibrium      393
Stable process      21
Standard one      28
starting      639
State      680
State constraints      129
State of infinity      24
State space      1
State vector      636
Stationary      2 3 404 405
Stationary independent increments      421
Steep      310
Stein’s lemma      411
Step size      246
Step size: local      246
Sticky boundary      28
Stieltjes integral      55 74
Stochastic approximation (see SA)      577
Stochastic basis      55
Stochastic control      180
Stochastic differential equation      391
Stochastic differential utitlies      706
Stochastic dominance      725 729
Stochastic evolution equatioin      219
Stochastic integral      32 69 71 72 90
Stochastic integral compensated      71
Stochastic integral componentwise      70 73
Stochastic integral vector      70
Stochastic labor income      707
Stochastic optimization      606 608 610 625
Stochastic partition      76
Stochastic processes      420
Stochastic Theta methods      247
Stochastic Volterra equation      224
Stochastically continuous      91
Stock      708
Stopping theorem      50
Stopping time      2 3 48
Stopping time problem      626
Strategy      485 521
Strategy: admissible      491 501 512
Strategy: admissible relaxed      502
Strategy: Markov      491
Stratonovich integral      82
Stratonovich SDE w.r.t. semimartingale      202
Stratonovich SDEs      167
Strong Markov property      2 3
Strong solution      84 161
Strongly continuous      23
Sub-additivity      398 405
Subjective discount rate      709
Subtraction: left      243
Subtraction: right      243
Sup norm      22
Super-replicates      741
Super-replicating      725 727 728
Superharmonic      176
Supermatingale      441
Supermeanvalued function      176
System identification      603
Tail probabilities      636
Tanaka — Meyer formulas      81
Taylor method      243 323
Theta — Euler method      259
Theta — Mil’shtein methods      253
Theta — Platen’s method      254
Thin set      53
Tight      376
Time homogeneous      161
Time-discretization      246
Tolerance      741
topology      635
Topology of pointwise convergence      389
Total number      243
Total variation distance      12
Tracking      605
Trading      712
Transaction costs      707 718 725
Transform: S      131
Transient      29 34 35
Transition matrix      635
Transition operator      22
Transition probability      1
Transition rates      9
Translation      143
Trapezoidal method: nonlinear-implicitly      259
Trivial      2
Trivial solution      438—440
Turnpike set      561—563 565 566 568
Two-dimensional      35
Two-point boundary      34
Types      366
Uniformly elliptic      38
unique      2
Uniqueness      161 374
Upper bound      364 365 375 381
Upper semicontinuous      380
Upper value      481
Upper value functon      481
User’s Guide by Crandall, Ishii and Lions      683
Usual conditions      55
Utility function      681
Value function      679 681 720 732
Van der Pol oscillator: modified      259
Varadhan’s lemma      380
Variational inequality      711
Verification result      715
Verification Theory      682
Version      51
Viscosity solution      190 682—684
Volatility      685 708 738 740
Volatility matrix      694
Wagner — Platen expansion      244
Weak convergence      588
Weak infinitesimal operator      423
Weak LDP      365 368 379 397
Weak solution      84
Weak topology      384 399 400 403
Wealth process      720
Well posed      37 38
Well-separating      382
Whiskers      152
White noise: measure      112
White noise: multiplication      145
White noise: space      112 117
Wick product      145
Wick tensor      118
Zero-transaction      734

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