Chueshov I. — Monotone Random Systems: Theory and Applications :: Электронная библиотека попечительского совета мехмата МГУ

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Chueshov I. — Monotone Random Systems: Theory and Applications

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Название: Monotone Random Systems: Theory and Applications

Автор: Chueshov I.

Аннотация:

The aim of this book is to present a recently developed approach suitable for investigating a variety of qualitative aspects of order-preserving random dynamical systems and to give the background for further development of the theory. The main objects considered are equilibria and attractors. The effectiveness of this approach is demonstrated by analysing the long-time behaviour of some classes of random and stochastic ordinary differential equations which arise in many applications.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 248

Добавлена в каталог: 12.05.2008

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Предметный указатель

$\mathbb{P}$ -complete $\sigma$ -algebra      19
$\mathbb{P}$ -completion of $\sigma$ -algebra      21
$\varphi$ -ergodic measure      51
$\varphi$ -invariant measure      51
Almost equilibrium      112
Bernoulli shifts      11
Binary biochemical model, random      17 30 58 62 94 97 102 110 114
Binary biochemical model, stochastic      72—74 79 94
Biochemical control circuit      2
Biochemical control circuit, random      171
Biochemical control circuit, stochastic      219
Borel $\sigma$ -algebra      9
Chapman — Kolmogorov equation      53
Cocycle      13
Comparison principle      109
Comparison principle, random      150
Comparison principle, stochastic      192
Competition and migration model      181
Cone, minihedral      87
Cone, normal      86
Cone, part of      84 91
Cone, regular      86
Cone, solid      83
Conjugacy of RDS      18
Cooperativity condition      147
Disintegration      51
Equilibrium      38
Equilibrium, stable, from above      107
Equilibrium, stable, from below      107
Equilibrium, stable, in probability      211
Equivalence of RDS      18
Fokker — Plank equation      204
Function, cooperative      147
Furstenberg — Khasminskii formula      75
Future $\sigma$ -algebra      52
Gonorrhea model      175 221
Gross-substitute system      178
interval      83
Interval, absorbing      108
Invariant measure      51
Irreducible matrix      147
Ito stochastic equation      71
Ito stochastic integral      67
Ito’s formula      69
Kick model      16 27 31 38 93
Lattice model      223
Liouville’s equation      58 73
Lyapunov exponent      60 75
Mapping, strongly positive      144
Mapping, sublinear      161 214
Mapping, weakly positive      144
Markov chain      15
Markov family      53
Markov measure      53
Martingale      67
MDS      see “Metric dynamical system”
MDS, ergodic      10
Measurable selection theorem      20
Metric dynamical system      10
Multifunction      18
Orbit      see “Trajectory”
Ornstein — Uhlenbeck process      79
Outer normal      61
Part (Birkhoff) metric      84
Past $\sigma$ -algebra      52
Perfection procedure      14
Polish space      13
Probability space      9
Process, adapted      66
Process, continuous      66
Process, predictable      66
Product $\sigma$ -algebra      9
Projection theorem      21
Radius of dissipativity      26
Random attractor      41

Random attractor, weak point      210
Random differential equation      56
Random Dirac measure      51
Random dynamical system      13
RDE      see “Random differential equation”
RDS      see “Random dynamical system”
RDS, -smooth      14
RDS, affine      14 46 138
RDS, asymptotically compact      31
RDS, compact      30
RDS, concave      114
RDS, conditionally compact      123
RDS, dissipative      26
RDS, linear      14 45
RDS, order-preserving      93
RDS, s-concave      116
RDS, strictly sublinear      113
RDS, strongly positive      105 145
RDS, strongly sublinear      114
RDS, sublinear      113
Scale function      203 206
SDE      see “Stochastic differential equation”
Semi-equilibria      95
Semimartingale      68
Separability set      21
Separable collection of random sets      21
Set, $\theta$ -invariant      10
Set, absorbing      26
Set, bounded from, above      84
Set, bounded from, below      84
Set, infimum of      84
Set, invariant      24
Set, invariant, backward      24
Set, invariant, forward      24
Set, lower bound      84
Set, maximal element of      84
Set, minimal element of      84
Set, omega-limit      34
Set, order-bounded      84
Set, random      18
Set, random, bounded      19
Set, random, closed      18
Set, random, compact      19
Set, random, tempered      23
Set, supremum of      84
Set, universally measurable      21
Set, upper bound      84
Skew-product semiflow      15
Spaces $C^{k,\delta}(I)$       199
Spaces $C^{k,\delta}_b$       70
Spaces $C^{k,\delta}_b(I)$       199
Speed measure      202 206
Stationary measure      50 53
Stochastic differential equation      70
Stopping time      67
Stratonovich stochastic equation      72
Stratonovich stochastic integral      68
Sub-equilibrium      95
Sub-equilibrium, absorbing      108
Super-equilibrium      95
Super-equilibrium, absorbing      108
Symbiotic interaction      176 222
Tail of trajectory      32
Tempered random variable      23
Top Lyapunov exponent      48 60 75
Trajectory      32
u-norm      84
u-subordination      84
Universal $\sigma$ -algebra      21
Universe      25
Walras’ law      178
White noise process      12
Wiener process      12 66
Wiener shift      12
Wong — Zaka? type theorem      77

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