The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Author(s): Jochen Blath, Peter Imkeller, Sylvie Roelly
Publisher: European Mathematical Society
Year: 2011
Language: English
Pages: 264
Tags: Математика;Теория вероятностей и математическая статистика;Теория случайных процессов;
Preface......Page 5
Contents......Page 7
The 33rd SPA Conference 2009......Page 9
Plenary Lectures......Page 12
Committees of the Conference......Page 14
List of Donors......Page 15
Introduction......Page 17
Formulation of the problem, assumptions and preliminary results......Page 19
Links to transportation-cost inequalities......Page 0
A Verification Theorem......Page 22
Existence of the processes (Y^1,…, Y^m)......Page 27
Connection with systems of BSDEs with oblique reflection......Page 29
Preliminaries......Page 30
Existence of a solution for the system of variational inequalities (19)......Page 33
General systems of BSDEs with oblique reflection......Page 39
Numerical schemes......Page 41
Introduction......Page 45
Background in discrete time ARCH and GARCH models......Page 46
Stationarity and tail behaviour in GARCH models......Page 47
Continuous time limits of GARCH models......Page 48
The COGARCH model......Page 49
A COGARCH option pricing model......Page 52
Relationship to other stochastic volatility models......Page 53
Default time and default adjusted return dynamics......Page 55
The risk-neutral dynamics and option pricing......Page 56
Variance-Gamma COGARCH......Page 57
Statistical estimation of COGARCH......Page 62
A method of moments estimation......Page 63
The ``first jump'' approximation for a Lévy process......Page 65
A discrete approximation to the COGARCH......Page 68
GARCH analysis of irregularly spaced data......Page 70
Definitions and results......Page 75
Exponential killing......Page 76
Exit independence between time and state......Page 77
The martingale property......Page 78
Trajectories that are never killed......Page 79
Lumping......Page 80
The parabolic Anderson problem......Page 83
The growth rate of the total mass......Page 86
Localisation: The one- and the two-cities theorem......Page 87
Scaling limit theorems......Page 91
Ageing in the parabolic Anderson model......Page 96
Conclusion......Page 99
Introduction......Page 103
Harris paths and tree profiles......Page 105
A discrete Ray–Knight theorem......Page 107
Subcritical branching: reweighting the excursions......Page 111
Bertoin's ``Trees of alleles with rare mutations''......Page 113
Feller branching with logistic growth, and Virgin Islands......Page 115
A Ray–Knight representation of logistic Feller branching......Page 118
Introduction......Page 123
The main idea......Page 125
Exchangeable pair coupling......Page 126
Stein's method for chi-square approximation......Page 127
Isonormal Gaussian processes......Page 128
Chaos decomposition in terms of multiple integrals......Page 129
Malliavin operators......Page 130
A basic result for the distance to normality......Page 132
Connections with exchangeable pairs......Page 133
Application to Poincaré-type inequalities......Page 134
Universality of Wiener chaos......Page 136
A bound on the distance to normal, and universality of Wiener chaos......Page 137
Generalizations......Page 139
Introduction......Page 143
Merging......Page 144
Stability......Page 145
Simple results and examples......Page 147
Weak ergodicity......Page 149
Products of stochastic matrices......Page 150
Product of random stochastic matrices......Page 152
Quantitative results and examples......Page 153
Singular values......Page 154
An example where stability fails......Page 156
Adapted kernels......Page 160
Time homogeneous results......Page 162
Time inhomogeneous chains......Page 163
Introduction......Page 169
The approach by Almgren and Chriss......Page 170
Maximization of the expected utility of revenues......Page 172
Second-generation market impact models......Page 177
Transient price impact in discrete time......Page 178
Transient price impact in continuous time......Page 186
Motivations......Page 197
Basic questions......Page 198
Dimension d=1......Page 199
Dimension d=2......Page 200
Continuous-time weakly self-avoiding walk......Page 201
Hierarchical lattice and walk......Page 202
Functional integral representation......Page 205
The renormalisation group map......Page 206
Results......Page 208
The lace expansion......Page 210
One idea from the proof of Theorem 8.1......Page 211
Conclusions......Page 212
Introduction......Page 217
Dirichlet Forms and symmetric Markov processes......Page 221
Generalized Feynman–Kac semigroups......Page 225
Donsker–Varadhan type large deviation principle......Page 228
L^p-independence of growth bounds......Page 231
A large deviation principle for normalized Markov processes......Page 237
Poincaré type inequality on Hilbert spaces......Page 243
Poincaré type inequality for Dirichlet forms......Page 246
Exponential decay of the semigroup in the tail norm......Page 249
Log-Sobolev inequality with unbounded below curvature......Page 254
Functional inequalities on non-convex manifolds......Page 256
List of Contributors......Page 263
