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

$(\mathcal{Y}_j,p_{ij})$       386
$A^{\delta}$       375
$B(\Sigma)$ -topology      387
      390
$C_b(\chi)$       381
      366
$d_\infty(\sigma,\sigma')$       403
$H(\nu)$       367
$H(\nu|\mu)$       367
      410
      391 410
      407
$I_k(\nu)$       402
$I_\infty(\nu)$       403
$I_{x,T}(f)$       391
$K_\alpha$       365
$L^\epsilon$       394
      391
      366
$L_\infty([0,1])$       388
$M_1(\Sigma)$       366
$Prob_\mu$       367
      386
$P_{\epsilon,m}$       378
$ri\mathcal{D}_{\Lambda^*}$       371
      410
$T_n(\nu)$       367
$U_{\phi,x,\delta}$       399
      394
      394
      390
$w_\epsilon$       390
$Z_\epsilon$       378
$\alpha_n$       410
$\beta_n$       410
$\chi$       363
$\chi^*$       383
$\delta$ -ergodic equilibrium      502 503
$\ell$ -separated      405
$\gamma$       363
$\gamma(\ell)$       405
$\Gamma^\sigma$       363
$\Gamma_\delta$       378
$\hat{S}_n$       396
$\hat{S}_n^m$       396
$\lambda$       94
$\Lambda(\lambda)$       368 369
$\Lambda^*(x)$       368
$\Lambda_0(\lambda)$       411
$\Lambda_f$       381
$\Lambda_n(\lambda)$       369
$\Lambda_{\mu_\epsilon}(\lambda)$       383
$\mathbb{C}$       372
$\mathbb{R}$       366
$\mathcal{AC}$       389
$\mathcal{A}$       375
$\mathcal{B}$       363
$\mathcal{B}_\chi$       363
$\mathcal{B}_\epsilon$       378
$\mathcal{B}_{\chi^n}$       396
$\mathcal{D}_I$       363
$\mathcal{D}_\Lambda$       369
$\mathcal{E}$       374
$\mathcal{F}$       370
$\mathcal{L}_N$       366
$\mathcal{M}$       407
$\mathcal{W}$       386
$\mathcal{W}'$       386
$\mathcal{Y}$       377
$\mu^n_{Y^k|A_\delta}$       407
$\mu_n$       368
$\mu_\epsilon$       363
$\nu_*$       407
$\nu_\epsilon$       390
$\overline{\Gamma}$       363
$\overline{\Lambda}(\lambda)$       383
$\overline{\Lambda}^*$       383
$\pi$ -mixing      405
$\pi_k(x,dy)$       402
$\Psi_I(\alpha)$       363
$\Sigma$       366
$\Sigma_\mu$       366
$\tau$ -topology      400 407
$\tilde{Z}_\epsilon$       378
$\underline{lim}$       386
$\varphi$ -irreducible      11
$\varphi$ -recurrent      11
$\{\mu_\epsilon\}$       378
$\{\tilde{\mu}_\epsilon\}$       378
${(\mathcal{B}_\chi)}^n$       396
Absolute      681
Absolutely continuous functions      388
Absorbing      27
Absorbing boundary conditions      7
Acceleration      637
Accessible      26
Accessible time      54
Adams method      257
Adapted      48 51
Adapted process      160
Adaptive beam forming      602
Adaptive control      603
Adaptive filtering      602
Adaptive schedules      645
Adjoint vector      431
Admissible control      432 537 539 543 548 551 562 569
Admissible controls      720
Admissible optimal control      435
Admissible policies      682
After      732
Aggregation      705
Algebraic dual      386
ALL      3
Alphabet      366
Analytic      126
Analytic bounds      735
Annihilation      142
Aperiodic      11
Arbitrary small      742
ARMA      16
ARMA Models      16
Aspiration level condition      634
Asymptotically stable      440
Asymptotically stationary      16
Autonomous      240
Autoregressive models      15
Autoregressive moving-average process      16
Average derivative      423
Backward Euler      247
Backward SDE      185
Backward SDE w.r.t. semimartingale      203
Backward SDE with jump      192
Bahadur and Rao      373
Balanced implicit methods      249
Baldi’s theorem      385
Banach space      397 407
Base      375
Basin      632
Basins      640
Bell numbers      123
Bennett’s Inequality      371
Best      637
Better      695
Birth-death chain      6
Black and Scholes      727
BOND      708
Borel      1
Borel $\sigma$ -field      363
Boundaries      6
boundary conditions      25

Boundary value problem      173
Bracket process      62 64 65
Brownian motion      390
Brownian motion process      421
Bryc’s theorem      382 404
Burkholder’s inequality      67
Buy      712
Cadlag process      53
Canonical      100
Canonical projections      403
Canonical representation      90
Capacity expansion      542
Cauchy problem      86
Center      23
Central limit theorem      372
Chapman — Kolmogorov      2
Chapman — Kolmogorov equation      8 22
Characteristic boundary      395
Characteristics      90 93
Chebycheff’s inequality      369 371
Chernoff’s asymptotic bound      411
Chernoff’s information      411
Chromosomes      658
Closed      23
Closed graph theorem      23
Closed loop      426
Co-state      431
Commutative noise      282
Compact subset      441
Compensator      59 88
Complementary hitting distribution      636
complete      55
Completely regular space      382
Compound Poisson      21
Conservative      26
consumption rate      722
Continuous martingale      62
Continuous part      54
Continuous-time SA      585
Contraction      22
Contraction principle      376
Contractivity      267
Contractivity: backward      309
Contractivity: forward      309
Contractivity: global      309
Contractivity: local      309
Control problem: stabilizing      426
Control process      680
Convergence w.p.1      588
Convex analysis      371
Convex dual      701
Convex function moderate      67
Convex good rate function      406
Convex rate function      370 376 383 387
Convolution      146
costs      740
Cramer’s theorem      368 385 396
Cross-over      658
CRRA      684
Cut off phenomena      40
Dawson — Gartner theorem      386
De Acosta      400
Decomposition      72
Definite: postive/negative      441
Degenerate elliptic      684
Delta      727
Denk — Hersch method      256 257
Depth      640 648
Derivative valuation      705
Derivative: Radon — Nikodym      130
Deterministic      426
Differential equation      430
Differential operator      393
Diffusion coefficient      28
Diffusion process      684 727
Directed weighted connection graph      635
Dirichlet problem      34
Discounted occupation measure      493
Discrepency      738
Discrete times      738
Dissipative      222
distribution      3
Distributions: tempered      111 112
Divergence      399
Doeblin minorization      11
Doleans exponential formula      79
Doleans exponential stochastic      79
Domain      363
Domain: attraction      438
Dominating payoff      724
Doob — Meyer’s decomposition      61
Drift velocity      28
Drift-implicit      247
du      401
Dual      721
Dual optional      59
Duality lemma      Ç84
Dynamic      645
Dynamic program      429
Dynamic Programing Principle      682
Dynamic programming      428
Ehrenfest model      7
Elliptic boundary      38
Embedded discrete      21
Empirical mean      364 365
Empirical measure      365 366 396 400
Energy      406 644
Entrance boundary      26
entropy      367
Equation depending on a parameter      165
Equidistant      246
Equilibrium asset      705
Equilibrium asset pricing      679
Ergodic      2
Ergodic cost criteria      706
Ergodic equilibrium      501
Ergodic optimal      497 502
Erogodic      11
Essential      11
Essentially smooth      370 387
Estimators      514
Euler method      246 247 301 323
Euler method: drift explicit-implicit      247
Euler method: implicit      247
Euler — Maruyama method      246
Euler — Runge — Kutta method      251
European call      725
Evanescent set      55
Evolutionary algorithm      612
Exact asymptotics      372
Exercise price      725
Existence      162
Existence and thm of SDE in hilbert S      222
Existence and uniqueness thm of SDE by nonlinear      210
Existence and uniqueness thm of SFDE      213
Existence of a LDP      375
Exit boundary      26
Exit from a domain      392
Explicit      24Ç
Explicit midpoint method      250
Explicit Theta methods      250
Explicit trapezoidal method      250
Explicit-implicit method      260
Explosion      28
Explosion time      9 33 37
Exponential approximation      376
Exponential tightness      375 383
Exponentially equivalent      378 389
Exponentially good approximation      378
Exponentially tight      365 400

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