Fayolle G., Iasnogorodski R., Malyshev V. — Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability) :: Электронная библиотека попечительского совета мехмата МГУ

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Fayolle G., Iasnogorodski R., Malyshev V. — Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)

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Название: Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)

Автор: Fayolle G., Iasnogorodski R., Malyshev V.

Аннотация:

Promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries, the authors use Using Riemann surfaces and boundary value problems to propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 167

Добавлена в каталог: 22.10.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abel's theorem      14
Abelian differential      14
Abelian differential of the first kind      49 55
Abelian differential of the third kind      56
Additive decomposition      63
Additive form      61 64
Algebraic extension of      62
Algebraic function      10 56 67 69
Algebraic solutions      67
Analytic continuation      35 125
Arbitrary genus      148
Asymptotics      145
Boundary value problem      93
Branch point      8
Branch points $x_{i}, y_{i}$       37
Branches of the algebraic function      10
Canonical functions      98
Carleman automorphism      106
Carleman — Dirichlet problem      105
Carleman's condition      103
Cauchy-principal value      97
Cauchy-type integrals      95
Conformal automorphisms      52
Continuation      122
Cover      8
Cover of S without branch point      37
Covering automorphism      12
Covering manifold      8
Critical points      10
CURVES      44
Cut      78
Cyclic group      58
Cyclic subgroup      29
Divisor      14 55
Elliptic function      15 36 66
Elliptic integrals      45
Elliptic modular functions      45
Ergodicity      142
Factorization      16
Factorization problem      93
Field of elliptic functions      36 73
Field of meromorphic functions      10 69
Field of rational functions      28 53
Finite extension      11
Finiteness of the group      54
Fractional linear transform      52 65 82
Fredholm integral equation      103
Functional equations      3
Fundamental equation      5 56
Fundamental form      5
Fundamental rectangle      76
Galois automorphisms      18
Galois extension      11 60
Galois group      11 60
General solution      74
Generating functions      94
Generator      60
Generators      29
Genus      13
Genus 0      129
Genus 1      35
Group of the random walk      27 29
Hadamard — Pringsheim theorem      86
Hilbert's theorem      60 64
Hoelder condition      96
Holomorphic      7
Holomorphic differential      13
Homographic      48
Homology basis      36
Homology class      31
INDEX      98 102 119 140 149
Index problem      150
Integral equations      93
Interval of the orbit      85

Invariant measure      3
Invariants      43
Jacobi elliptic function      132
Legendre's identity      71
Leray residues      148
Lie over      8
Lifting      9 18
Lifting of the automorphisms      37
Liouville's theorem      99
Logarithmic singularities      56
Mapping      7
Martin boundary      148
Meromorphic      8
Modular functions      49
Monodromy theorem      10 41
Multiplicative decomposition      61
Multiplicative form      61
Norm      58 61
normal      11
Orbit      83 84
Order of $\mathcal{H}$       52
Pair of primitive periods      45
Period parallelogram      36 45
Periods $\omega_{1}$ , $\omega_{2}$       36
Plemelj formulae      96
Poncelet's problem      55
Principal divisor      14 55
Problem of abelian integrals      55
Product form of Jackson's networks      91
Projection      8
Proper mapping      8
Proper unbranched covering      9
Quartic curves      112
Queueing      54 88
Random walk      18 21 89
Rational probabilistic solutions      83
Rational solution      56 64 65
Reduced index      119 141
Reduction of the index      122
Regular point      8
Residues of the meromorphic function      76
Reversible random walks      79
Riemann sphere      33
Riemann surface      7
Riemann surface of the algebraic function      11
Riemann — Carleman BVP      102
Riemann — Hilbert — Carleman      95
s-sheeted covering      8
Saddle-point      148
Sectionally holomorphic      97
Series representation      135
Shift      103
SIMPLE      21
Simple random walk      54 84 116
Simply-connected      142
singular      18
Singular integrals      95
Singular random walks      115
Slit      94
Sokhotski — Plemelj formulae      97 98
Steepest descent point      148
Torus      31
Trace      58 61
Uniformizatioii      13 43 89 135
Unimodular transformation      35 42
Universal cover      12
Universal covering      8 66 69
Variation of the argument      77
Weierstrass $\wp$ -function      43 66
Weierstrass $\zeta$ -function      70
Weierstrass canonical form      44
Weierstrass domain      44 45
Weierstrass elliptic function      42
Wiener — Hopf factorization      149

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