Content -- Preface -- List of participants -- Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles Shigeki Aida -- 1. Introduction -- 2. Elworthy and Truman's formula and estimates on heat kernels -- 3. Rotationally symmetric case -- References -- Equivalence of bipartite quantum mixed states under local unitary transformations Sergio Albeverio, Shao-Ming Fei and Xiao-Hong Wang -- Abstract -- References -- Invariant Gibbs measures for the 2D vortex motion of fluids Sergio Albeverio and Benedetta Ferrario -- Abstract -- 1. Introduction -- 2. Gibbs measures of compound Poisson type -- 3. Deterministic dynamics of vortices -- 4. Classical pre-Dirichlet forms given by the Gibbs measures -- Acknowledgments -- References -- Limit laws for sums of random exponentials Gerard Ben Arous, Leonid Bogachev and Stanislav Molchanov -- Abstract -- 1. Introduction -- 2. Regularity and Kasahara's Tauberian theorem -- 3. 'Crude' limit theorems above the critical points -- 4. Normalized regular variation -- 5. Limit theorems below the critical points -- 6. Model example: Weibull's distribution -- 7. Sketch of the proofs -- 8. Limit distribution of the maximum -- Acknowledgments -- References -- Thin-Film-Growth-Models: On local solutions Dirk Blomker and Gugg Christoph -- Abstract -- 1. Introduction -- 2. Assumptions -- 3. Global solutions -- 4. Local existence in H1 -- 5. Local existence in W1,4 -- References -- Asymptotic behaviour of solutions to the 2D stochastic Navier- Stokes equations in unbounded domains - new developments Brzniak Zdzistaw and Yu-Hong La -- Abstract -- 1. Introduction -- 2. Preliminaries on RDS's -- 3. RDS generated by SNSEs -- 4. Random absorbing set for RDS generated by NSEs -- 5. Weak sequential continuity of RDS generated by NSEs -- 6. Asymptotic compactness of the RDS generated by the NSEs.

7. Invariant measures -- Acknowledgments. -- References -- Stochastic models of economic optimization Mu-Fa Chen -- Abstract -- 1. Input-output method -- 2. L. K. Hua's fundamental theorem -- Stability of economy -- Economy in markets -- 3. Stochastic model without consumption -- 4. Stochastic model with consumption -- 5. Proof of Theorem 3.1 -- Acknowledgment. -- References -- A note on the Green function estimates for symmetric stable processes Zhen-Qing Chen and Ren-Ming Song -- Abstract -- References -- Ornstein-Uhlenbeck semigroups on Riemannian path spaces Ana Bela Cruzeiro and Xi-Cheng Zhang -- 1. Introduction -- 2. The Riemannian path space -- 3. Finite dimensional approximations -- 4. Strong convergence results -- 5. The lifted semigroup -- Acknowledgement: -- References -- Essential spectrum on Riemannian manifolds K. D. Elworthy and Feng-Yu Wang -- Abstract -- 1. Introduction -- 2. Proofs -- 3. Extensions -- 4. The essential spectrum on one-forms -- Acknowledgment. -- References -- Levy process on real Lie algebras Uwe Franz -- Abstract -- 1. Introduction -- 2. Levy processes on real Lie algebras -- 3. Examples -- 3.1. The Heisenberg- Weyl algebra and the oscillator algebra -- 3.2. The Lie algebra sl (2,R) -- 4. KMS states -- References -- Zeros of eigenfunctions of the generator of a gap diffusion Uta Freiberg and Jorg-Uwe Lobus -- Abstract -- 1. Introduction -- 2. Preliminaries -- 2.1. Definition of the operator -- 3. Spectral asymptotics in the self-similar case -- 3.1. Self-similar sets and self-similar measures -- 3.2. Spectral asymptotics -- 4. Zeros of eigenfunctions -- 4.1. Number of zeros -- 4.2. The asymptotic distribution of the zeros in the self-similar case -- References -- Wick rotation for holomorphic random fields Hanno Gottschalk -- Abstract -- 1. Introduction -- 1.1. Motivation -- 1.2. Outline -- 2. Preparations.

2.1. Random point measures -- 2.2. Holomorphic functions -- 3. Ferromagneticity and TD limit -- 3.1. A general strategy -- 3.2. Weakly attractive interaction -- 4. Connection with field theory -- 4.1. Convoluted random point measures and local interactions -- 4.2. Connections to Widom-Rowlinson and Potts models -- 5. Holomorphic paths and Wick rotation -- 5.1. Pathwise analytic continuation -- 5.2. Analyticity of Schwinger functions and relativistic invariance -- 5.3. Examples -- 5.4. The Wick rotated measure - failure of invariance -- Acknowledgments. -- References -- White noise approach to interacting quantum field theory Zhi- Yuan Huang and Guang-Lin Rang -- Abstract -- 1. Introduction -- 2. General White Noise Approach to Construction of Interacting Quantum Field Theory -- 3. Two Examples -- 3.1. P( )2 Quantum Field -- 3.2. ( )44 Quantum Field -- 3.3. The Dynamical Properties of Interacting Quantum Field -- References -- Generalized Hormander theorem for non-local operators T. Komatsu and A. Takeuchi -- Abstract -- 1. Variation for SDE with jumps -- 2. Formulas of integration by parts -- 3. Estimation for semi-martingales -- 4. Generalized Hijrmander condition -- References -- Stochastic mollifier and Nash inequality Remi Leandre -- 1. Introduction -- 2. The main localizing lemma -- 3. Varadhan estimates without boundedness assumption -- 4. Asymptotic expansion without boundedness assumption -- 5. Non exponential decay without boundedness assumption -- References -- Precise estimations related to large deviations Song Liang -- 1. State of the problems -- 2. o(1) Order estimations for the i.i.d. case -- 3. Asymptotic expansions for the i.i.d. case -- 4. o(1) Order estimations for diffusion processes on toruses -- References -- Central limit theorems for generalized set-valued random variables S. Li, Y. Ogura, F.N. Proske and M. L. Puri.

1. Introduction -- 2. Preliminaries on Generalized Set-Valued Random Variables -- 3. Central Limit Theorems for Generalized Set-Valued Random Variables -- References -- Littlewood-Paley-Stein inequalities and Riesz transforms on complete Riemannian manifolds Xiang-Dong Li -- Abstract -- 1. Introduction -- 2. The basic lemma -- 3. Semigroup domination inequalities -- 4. Littlewood-Paley-Stein inequalities -- 5. An effective sufficient condition -- 6. Manifolds satisfying the Sobolev inequality -- Acknowledgement. -- References -- The ground state in Nelson's model with or without infrared cutoff Jozsef Lorinczi -- Abstract -- 1. Introduction -- 2. Basic processes for particle and field -- 3. The infrared divergent case: d = 3 -- 4. The infrared convergent case: d 4 -- 5. 3D infrared regular representation -- Acknowledgments: -- References -- Optimal filtering of stochastic parabolic equations S. V. Lototsky -- Abstract -- 1. Introduction -- 2. Stochastic Parabolic Equations With Random Coefficients -- 3. Optimal Nonlinear Filtering of Diagonalizable Equations -- 4. Linear Filtering -- References -- A new example of interacting free Fock space Y.G. Lu and S. Ruggeri -- Abstract -- 1. Introduction -- 2. Some preparations -- 3. The distribution of field operator -- References -- Stochastic holonomy Itaru Mitoma -- 1. Introduction -- 2. Definitions and Results -- References -- On the stochastic transport equation of convolution type Habib Ouerdiane and Jose Luis Silva -- Abstract -- 1. Introduction -- 2. Preliminaries -- 2.1. Test and generalized functions spaces -- 2.2. The Convolution Product -- 3. Applications to the stochastic transport equation -- 4. The solution of the transport equation as limit of integrals -- Acknowledgments -- References -- Forward growth rates: connecting the HJM and the BS models Alex Stefan Popovici -- Abstract.

1. Introduction -- 2. A short review of zero coupon bonds, forward interest rates and the HJM framework -- 3. Forward growth rates for the asset value of a company -- 4. HJM-type dynamics of the discounted forward growth rates and the connection to the BS model -- 5. Modelling discounted growth coefficients by Levy processes -- 6. European option prices and comparison with the BS-formula -- 7. Conclusion -- Acknowledgements -- References -- Independence and product systems Michael Skeide -- Abstract -- 1. Independence -- 2. Conditional independence -- 3. Dilations -- References -- Brownian motion close to submanifolds of Riemannian manifolds N . Sidorova, O. G. Smolyanov, H. V. Weizsacker, O. Wattich -- Abstract -- 1. Introduction -- 2. Minkowski Regularity -- 3. Confinement to Submanifolds in Classical and Quantum Mechanics -- 4. Conditional Probability -- 5. Two Limits -- 6. The Effective Potential -- 7. Computing Veff -- References.