Whitt W. — Stochastic-process limits and application to queues :: Электронная библиотека попечительского совета мехмата МГУ

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Whitt W. — Stochastic-process limits and application to queues

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Название: Stochastic-process limits and application to queues

Автор: Whitt W.

Язык:

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 617

Добавлена в каталог: 15.06.2005

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Предметный указатель

, closure of A      3
$A^{\epsilon}$ , $\epsilon$ -open nbhd.      2
$C_0 \equiv C\cap D_0$       164
$C_m \equiv C\cap D_m$       164
$C_{\uparrow\uparrow} \equiv C\cap D_{\uparrow\uparrow}$       164
$C_{\uparrow} \equiv C\cap D_{\uparrow}$       164
$D([0,\infty), \mathbb{R}^k)$       142 216
, graph subsets      129
, subset of       184
, jumps up      215
, subset with $x(0) \geq 0$       164
, jumps in one coord.      214
, piecewise-const. fcts.      116
, piecewise-linear      208
, monotone, all i      164
, product metric      121
, subset of D with discs, at rationals      25
, jumps same sign      205 215
, x in unbded above      183
$d_{J_1}(x_1, x_2)$ , metric      25
$D_{l,r}$ , limits either left or rt.      248
$D_{lim}$ , fcts. with left and rt. lims.      243
$d_{M_1}(x_1, x_2)$ , metric      25 118
$d_{s,2}(x_1, x_2)$ , distation      148
$D_{s,l} \equiv D_s\cup D_l$       208
$d_{s}(x_1, x_2)$ , metric on D      118
$D_{u,\epsilon}$ , subset of       184
$D_{u\uparrow\uparrow} = D_u\cup D_{\uparrow\uparrow}$       183
$D_{u\uparrow} = D_u\cap D_{\uparrow}$       183
$D_{u\uparrow}^*$ , subset of $D_{u\uparrow}$       184
$d_{w,2}(x_1, x_2)$ , distation      148
$d_{w}(x_1, x_2)$ , distation on D      118
$D_{\uparrow\uparrow}$ , increasing x in $D_{\uparrow}$       164
$D_{\uparrow}$ , nondecreasing x in       164
$F^{-1}(t)$ , rt.-cont. inverse      6
- thick graph      117
, thick graph      117
$L = \lambda W$       52 71
topology on D      210
topology on $D([0,\infty), \mathbb{R})$       186
metric on D      118
topology on $D([0, \infty), \mathbb{R})$       186
metric on D      144
, metric on D      144
//1 queue      262
, product metric on D      145
$M_{t_1,t_2}$ , local max fct.      160
$N(m, \sigma^2)$ , normal variable      23
, in-prob. dist.      17
$Q \equiv P^t$ , reflection matrix      197
$Q \equiv \lim_{t\downarrow 0}(P(t)-I)$       33
$R \equiv (\psi, \phi)$ , multiplication ref. map      197
$R \equiv (\psi,\phi)$ , mult. ref. map      197
$r_{t_1,t_2}$ , restriction map      143
, convergence characteristic by linear maps      136
, convergence characteristic of main theorem      128
, convergence characteristic visits to strips      138
, metric      118
, convergence characteristic by extrema      160
, convergence characteristic by linear maps      159
, convergence characteristic of main theorem      149
, metric      145
, parametric representation      148
, topology      144
$u(x_1, x_2, t, \delta)$ , unif. distation fct.      124
$v(x_1, x_2, t, \delta)$ , unif. distation fct.      125
$v^{a,b}_{t_1,t_2}(x)$ , visits to strip [a, b]      137
, convergence, characterizations of      155
, convergence, inherit jumps from      157
, convergence, pres. within bnding fcts.      161
, parametric representation      148
, topology      144
$w_s(x, t, \delta)$ , oscilation fct      125
$w_s(x, \delta)$ , oscilation fct      128
$w_w(x, t, \delta)$ , oscilation fct      125
$w_w(x, \delta)$ , oscilation fct      131
$x\dot y$ , composition      164
$x^{-1}$ , inverse map      183
$x^{\uparrow}$ , supremum map      52 173
$Y = \lambdaX$       72
$Z \equiv (I-P +\Pi)^{-1}$ , for DTMC      31
$z_{\epsilon}\equivz_{\epsilon}(x,y)\equiv\epsilon^{-1}[(x+\epsilon y)^{\uparrow} - x^{\uparrow}]$       243
$\bar{d}(A, G_x)$ , order-const, distation      131
$\bar{d}(A, \Gamma_x)$ , order-consist, distation      119
$\bar{w}_s(x_1,x_2,t,\delta)$ , oscilation fct      125
$\bar{w}_w(x_1,x_2,t,\delta)$ , oscilation fct      125
$\beta_t: [0,1] \rightarrow [0,1]$       123
$\delta_s$ , Dirac measure      10
$\Gamma$ , scaling matrix      75
$\gamma_n$       101
$\Gamma_x$ , thin graph      117
$\Lambda(\mathbb{R}_+)$ , homeomorphisms      51
$\mathcal{G}$ , set of real-val. fcts.      2
$\mathcal{P} = \mathcal{P}(S)$       1
$\mathcal{R}(\alpha)$ , regularly varying      52
$\mu_s(x_1,x_2)$ , distantion      144
$\nabla_g(\mu)$ , gradient      88
$\partial A$ , boundary of A      8
$\Phi$ , std. normal cdf      24
$\phi(x) \equiv x + (-x\vee 0)^{\uparrow}$ , one-dimensional reflection map      181
$\Phi^L_x(t)$       244
$\Phi^R_x(t)$       244
$\phi_K: D\rightarrow D$ , ref. map      26
$\Phi_x(t)$       244
$\pi(P_1,P_2)$ , Prohorov metric      1
$\pi\equiv \pi_{x,Q}:D^k_{\uparrow}\rightarrow D^k_{\uparrow}$       199
$\Pi_s(x)$ , set of strong par. representation      118
$\Pi_w(x)$ , set of weak par. representation      118
$\Pi_{s,2}(x)$ , parametric representation      148
$\Pi_{w,2}(x)$ , par. representation      148
$\pi_{\gamma}(P_1,P_2)$ gen. Proh. metric      3
$\psi(s) \equiv \log Ee^{-sL(1)}$ , Laplace exponent      99
$\Psi(x)$ , feas. regulator set      197
$\rho(G_x)$ , thick range      117
$\rho(\Gamma_x)$ , thin range      117
$\Rightarrow$ , weak convergence      1
$\xi_n$       101
=, equality in distribution      23
Abate      22 44 48
Adaptedness of ref. map      202
Addition, continuity of, for       135 136
Addition, continuity of, for       159
Addition, measurability of      136
Adjoint space      16
Albert      87
Analytic method      22
Anscombe      71 87
Approximation of functions in by fcts. in $D_{s,l}$       208
Approximation of functions in D by fcts. in       116
Approximation of graphs by finite sets      119
ARMA (p, q)      47
arrivals      52 (see also “Time averages ASTA”)
Asmussen      36
ASTA      52
Asymptotic efficiency of simulation estimators      73
Asymptotic equivalence of cting. and inv. fcts.      192
Asymptotic validity of seq. stop rule      78
Asymptotic variance      30
Asymptotic variance for a birth-and-death pr.      35
Asymptotic variance for the M/M/l queue      35
Autocovariance function      34
Autoregressive moving average, ARMA      47
B(x, $\epsilon$ ), open ball      5
B*, adjoint space      16
Baccelli      71
Backshift operator      47
Bad(x), set of bad pts.      248
Banach space, perspective on “weak”      16
Batch Markovian arrival pr.      39
Beran      47 50

Berry — Esseen theorem      24
Bertoin      41 43 100
Billingsley      19—22 40 165 166
Bingham      81 98
Birth-and-death process      35
Birth-and-death process, asymptotic variance for      35
BMAP, batch Mark, arrival pr.      39
Bondesson      44
Book, Appendix A      52 79 80 85
Book, Chapter 11      27
Book, Chapter 12      v 113
Book, Chapter 13      iv v 38 51 163 235 237 277
Book, Chapter 14      v 195
Book, Chapter 3      iii 27
Book, Chapter 4      iv 23
Book, Chapter 5      v 97 196
Book, Chapter 7      23
Book, Chapter 8      v 97
Book, Chapter 9      v 97
Book, condition 12.5.4      177
Book, condition 12.5.5      177
Book, Corollary 12.11.2      213
Book, Corollary 12.11.4      103
Book, Corollary 12.11.6      161 193
Book, Corollary 12.5.1      174 212
Book, Corollary 13.4.1      236
Book, Corollary 13.7.1      236
Book, Corollary 13.7.2      236
Book, Corollary 14.3.2      225
Book, Corollary 14.3.4      211
Book, Corollary 14.3.5      216
Book, equation 11.5.3      125
Book, equation 11.5.4      144
Book, equation 12.4.1      168
Book, equation 12.4.3      168 171
Book, equation 12.4.4      170 171
Book, equation 12.5.3      103
Book, equation 13.4.1      238
Book, equation 13.5.1      238
Book, equation 14.2.35      216
Book, equation 14.2.6      216
Book, equation 14.8.6      227
Book, equation 2.3.6      26
Book, equation 3.3.2      114 121 181
Book, equation 3.3.4      118 181
Book, equation 4.5.12      43
Book, equation 4.5.13      43
Book, equation 4.6.13      50
Book, equation 4.6.6      46
Book, equation 4.7.1      50
Book, equation 5.2.5      181
Book, Example 1.4.2      47
Book, Example 12.10.1      145
Book, Example 12.3.1, 121      214
Book, Example 14.5.3      213
Book, Figure 11.2      113
Book, Figure 13.1      191
Book, Lemma 12.4.2      169
Book, Lemma 12.5.1      160
Book, Lemma 13.4.1      239
Book, Lemma 13.5.1      239
Book, Lemma 13.6.3      190
Book, Lemma 13.8.1      55
Book, Lemma 14.3.3      225
Book, Lemma 14.3.4      208 210
Book, Proposition 13.2.1      82
Book, Section 1.3      7
Book, Section 1.4      7 23
Book, Section 10.4.4      iv 73
Book, Section 11.2      139
Book, Section 11.5      144
Book, Section 11.6      114 221
Book, Section 12.11      163
Book, Section 12.2      255
Book, Section 12.4      166 168
Book, Section 12.6      134 163
Book, Section 12.7      102 163
Book, Section 12.9      144
Book, Section 13.4      259
Book, Section 13.6      187 268
Book, Section 13.7      62 102 190
Book, Section 13.8      55 102
Book, Section 14.2      204
Book, Section 14.6      196 218 233
Book, Section 14.7      233
Book, Section 2.3      26 196
Book, Section 3.2      25
Book, Section 3.4      17
Book, Section 3.5      51 163 235
Book, Section 4.3      23 41
Book, Section 4.4      30 41 90
Book, Section 4.5      41
Book, Section 4.6      23 50
Book, Section 4.7      23 41 50
Book, Section 5.9      iv 36 73
Book, Section 7.3      190
Book, Section 8.5      22
Book, Theorem 11.3.1      5 9
Book, Theorem 11.3.4      20 21 76
Book, Theorem 11.3.5      17
Book, Theorem 11.4.5      77 85
Book, Theorem 11.5.2      164
Book, Theorem 11.5.3      164
Book, Theorem 11.6.1      221 231
Book, Theorem 11.6.7      221
Book, Theorem 12.11.1 (v)      167
Book, Theorem 12.11.2 (iv)      167
Book, Theorem 12.2.2      175
Book, Theorem 12.4.1      169 172 177
Book, Theorem 12.5.1      103 105 177 255 258
Book, Theorem 12.5.1 (v)      167 212
Book, Theorem 12.5.2 (iv)      167
Book, Theorem 12.7.3      102
Book, Theorem 12.9.4      217
Book, Theorem 13.2.3      81 85
Book, Theorem 13.3.2      71 236 263 264
Book, Theorem 13.4.1      54
Book, Theorem 13.6.2      270
Book, Theorem 13.6.3      269 275
Book, Theorem 13.7.2      109 236
Book, Theorem 13.7.4      v 105 108 236
Book, Theorem 13.8.2      62
Book, Theorem 14.2.4      225
Book, Theorem 14.2.5      214 216
Book, Theorem 14.2.9      195 216
Book, Theorem 14.4.1      211
Book, Theorem 14.4.2      213
Book, Theorem 14.4.2 (a)      215
Book, Theorem 14.4.3      215 216
Book, Theorem 14.8.1      226
Book, Theorem 14.8.3      227
Book, Theorem 14.8.6      226
Book, Theorem 3.2.1      1
Book, Theorem 3.2.2      6
Book, Theorem 3.4.2      25 26
Book, Theorem 3.4.3      19
Book, Theorem 3.4.4      20
Book, Theorem 4.3.2      86
Book, Theorem 4.3.5      87
Book, Theorem 4.4.2      31
Book, Theorem 4.4.4      40
Book, Theorem 4.6.1      50
Book, Theorem 5.2.1      80
Book, Theorem 5.8.2      99
Book, Theorem 8.3.1      v 100
Book, Theorem 8.5.2      99
Book, Theorem A.5      53
Borel — Cantelli theorem      28
box      47 48
Bratley      75 87

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