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| Whitt W. — Stochastic-process limits and application to queues |
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| Предметный указатель |
Prabhu 99 100
Preservation of parametric representation by reflection 205
Preservation of ptwise. converg. 51
Product, measure 10
Product, metric 145
Product, space 10
Prohorov 1—6 139
Prohorov metric 2 17 25
Projection map 26
Puhalskii v 97 105 108 110 111 186 277
Queueing network 233
Queueing networks 217
rad(A), radius of A 8
Radius of a set 8
Random measure 43
Random sum 37 164
Random time change 72 164
Range, thick 118
Range, thin 117
Rates of convergence for heavy-traf. limits 26
Rates of convergence in CLT 24
Rates of convergence in FCLT 25
Reflected Levy process 22 98
Reflected Levy process, steady-state distribution 98
Reflected process, limiting stationary version 218
Reflected process, tightness of marginals 221
Reflection map 26
Reflection map, multidimensional see “Multidim”
Reflection map, one-sided, one-dimimensional 181—183
Reflection map, one-sided, one-dimimensional,  -cont. fails 181
Reflection map, one-sided, one-dimimensional, convergence pres. with ctring. 182
Reflection map, one-sided, one-dimimensional, derivative of 259
Reflection map, one-sided, one-dimimensional, Lipschitz property 181
Reflection of a parametric representation 204
Reflection, matrix 197
Reflection, matrix, norm 200
Reflexive space 17
Regenerative cycles 36
Regenerative process 36
Regenerative structure 30
Regularly varying see “Appendix A”
Regularly varying function 52
Reiman 112
Reinsel 47 48
Remainder processes 37
Renewal process 37
Renewal-reward processes 194
Rescaling of mult. ref. map 202
Resnick 92 93
Restriction of fct. 143
Revesz 27—29
Rinc(x), rt. inc. pts. of a; 248
Robbins 87
Robbins — Monro stochastic approx. 91
Rogers 100
Ruppert 91 92
Samorodnitsky 47 50 100
Sample mean of IID random variables 86
Sample mean of IID random vectors 87
Sample mean with infinite variance 93
Sample mean, functions of 88
Sample-path method 22
Sauer 75 88 110
Schrage 75 87
Schwartz 16
Segment, product 117
Segment, standard 117
Semimartingales 46
Separable metric space 1
Sequential stopping rule, absolute-precision 77
Sequential stopping rule, relative-precision 78
Service interruptions 217
Set of discontinuity points 115
Set, feasible regulator 197
Shiryaev 40—42 45 46 111 142 178
Siegmund 87
Signed measures 16
Simmons 16
Simulation, application of limits to 73
Simulation, run length 74
Simulation, sequential stopping rules, asymptotic validity 73
Skorohod 6—16 29 45 121 128 129 137 144 149 155 160 161 194
Skorohod, embedding theorem 29
Skorohod, representation theorem 2 6
SLLN and FSLLN equivalence 53
Smorodinskii 111
| Snell 31 33
Space, topological, of sets 246
Space, topological, topologically complete 139
Srivastava 87
Stable innovations 50
Starica 92 93
Starr 87
Stationary process 218
Steady-state distribution of a reflected Levy process 98
Steady-state distribution, steady-state mean estimating 89
Stidham 52 54 71 72 164
Stochastic approximation, Kiefer — Wolfowitz 91
Stochastic approximation, Robbins — Monro 91
Stochastic fluid networks 217
Stolyar 112
Stout 27
Strassen representation theorem 17
Strengthening mode convergence 134
Strong approximations 27
Strong dependence 46
Supremum map 54 173—180
Supremum map, convergence pres., centering 174
Supremum map, criterion for joint convergence 178
Supremum map, ctring in other direction 180
Supremum map, derivative of 243
Switching u and r in parametric representation of inverse fct. 184
Takacs 98 100
Taqqu 47 50 100
Teugels 81
Theorem, Berry — Esseen 24
Theorem, Borel — Cantelli 28
Theorem, continuous-mapping 17 19
Theorem, Donsker’s 25
Theorem, Egoroff’s 12
Theorem, gen. cont.-mapping 20
Theorem, Helly selection 140
Theorem, Lipschitz-mapping 17 26
Theorem, Prohorov metric 2
Theorem, Skorohod embedding 29
Theorem, Skorohod representation 2 6
Theorem, Strassen representation 17
Theorem, strong approximation 27
Thick graph 117
Thick range 118
Thin graph 117
Thin range 117
Thorin 44
Tightness of a reflected process 221
Topologically complete 139
Totally skewed Levy motion 43
transform 22
triangular arrays see “Double sequences”
Triple of characteristics for Levy process 42
Truncation function for Levy process 42
Tusnady 27
Two-sided regulator 217
Uniform, convergence of integrals 2
Uniform, distance functions 124
Uniform, metric 114
Uniform, metric for cdf’s 18 24
Uniform, norm 16
Uniformly bounded 2
Upper semicontinuity of max. abs. jump fct. 157
Upper semicontinuity, preservation by infimum 198
Useful functions 194
v(x;A), modulus of cont. 116
Venter 91 92
Virtual Mark, arriv. pr. see “BMAP”
Volume of confidence set 74
Volume of confidence set, convergence characteriz. of 131
Volume of confidence set, topology 118
Wang 27
Weak consistency a counterexample for 94
Weak convergence 1 16
Weak dependence 30
Weak topology 17
Weak* topology 17
Welch 75
Wetherill 87
Wichura 6
x(t-), left limit 114
Z(S), finite signed measures 16
Zhang 27
Zolotarev 98
[a, b], standard segment 117
[[a, b]], product segment 117
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