Probability and Partial Differential Equations in Modern Applied Mathematics

1. Nonnegative Markov Chains with Applications
K. S. Athreya

2. Phase Changes with Time and Multi-Scale Homogenizations of a Class of Anomalous Diffusions
Rabi Bhattacharya

3. Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes
Rabi Bhattacharya, Larry Chen, Ronald B. Guenther, Crris Orum, Mina Ossiander, Enrique Thomannii, Edward C. Waymire

4. Amplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures
Dirk Blömker, Martin Hairer

5. Enstrophy and Ergodicity Of Gravity Currents
Vena Pearl Boncolan-Walsh, Jinqiao Duan, Hongjun Gao, Tamay Özgökmen, Paul Fischer, Traian Iliescu

6. Stochastic Heat and Burgers Equations and Their Singularities
Ian M. Davies, Aubrey Truman, Huaizhong Zhao

7. A Gentle Introduction to Cluster Expansions
William G. Faris

8. Continuity of the Itô-Map for Holder Rough Paths with Applications to the Support Theorem in Holder Norm
Peter K. Friz

9. Data-Driven Stochastic Processes in Fully Developed Turbulence
Martin Greiner, Jochen Cleve, Jürgen Schmiege, Katepalli R. Sreenivasan

10. Stochastic Flows on the Circle
Yves Jaw, Olivier Raimond

11. Path Integration: Connecting Pure Jump and Wiener Processes
Vassili N. Kolokoltsov

12. Random Dynamical Systems in Economics
Mukul Majumdar

13. A Geometric Cascade for the Spectral Approximation of the Navier-Stokes Equations
M. Romito

14. Inertial Manifolds for Random Differential Equations
BjÖrn Schmalfuss

15. Existence and Uniqueness of Classical, Nonnegative, Smooth Solutions of a Class of Semi-Linear Spdes
Hao Wang

16. Nonlinear Pde’s Driven by Lévy Diffusions and Related Statistical Issues
Wojbor A. Woyczynski

Keywords: Mathematics, Partial Differential Equations, Applications of Mathematics, Probability Theory and Stochastic Processes