Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Dan Crisan
Integration by Parts Formula with Respect to Jump Times
for Stochastic Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Vlad Bally and Emmanuelle Cl´ement
A Laplace Principle for a StochasticWave Equation in Spatial
Dimension Three . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
V´ıctor Ortiz-L´opez and Marta Sanz-Sol´e
Intertwinned Diffusions by Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Xue-Mei Li
Efficient and Practical Implementations of Cubature on
Wiener Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Lajos Gergely Gyurk´o and Terry J. Lyons
Equivalence of Stochastic Equations and Martingale Problems . . . . . . . . . . . . . .113
Thomas G. Kurtz
Accelerated Numerical Schemes for PDEs and SPDEs . . . . . . . . . . . . . . . . . . . . . . . .131
Istv´an Gy¨ongy and Nicolai Krylov
Coarse-Grained Modeling of Multiscale Diffusions:
The p-Variation Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
Anastasia Papavasiliou
Numerical Solution of the Dirichlet Problem for Linear
Parabolic SPDEs Based on Averaging over Characteristics . . . . . . . . . . . . . . . . . . .191
Vasile N. Stanciulescu and Michael V. Tretyakov
vii
viii Contents
Individual Path Uniqueness of Solutions of Stochastic
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .213
AlexanderM. Davie
Stochastic Integrals and SDE Driven by Nonlinear L´evy Noise . . . . . . . . . . . . . .227
Vassili N. Kolokoltsov
Discrete Algorithms forMultivariate Financial Calculus . . . . . . . . . . . . . . . . . . . . .243
Radu Tunaru
Credit Risk, Market Sentiment and Randomly-Timed Default . . . . . . . . . . . . . . .267
Dorje C. Brody, Lane P. Hughston, and Andrea Macrina
Continuity of Mutual Entropy in the Limiting Signal-To-Noise
Ratio Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281
Mark Kelbert and Yuri Suhov