Existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional nonlinear stochastic fractional partial differential equations of order [alpha]1 containing derivatives of entire order and perturbed by space-time white noise are studied. The fractional derivative...

The problem of reconstructing the drift of a diffusion in , d[greater-or-equal, slanted]2, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of parabolic partial differential equations. This...

We study the speed of convergence of the explicit and implicit space-time discretization schemes of the solution u(t,x) to a parabolic partial differential equation in any dimension perturbed by a space-correlated Gaussian noise. The coefficients only depend on u(t,x) and the influence of the...

We prove, using coupling arguments, exponential convergence to equilibrium for reaction-diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.

The conservation of continuous symmetries in two-dimensional systems with interaction is a classical subject of statistical mechanics. So far, all results of this sort required some smoothness properties of the interaction. Only recently Ioffe et al. (Comm. Math. Phys. 226 (2002) 433) succeeded...

We prove a symmetry relationship between floating strike and fixed strike Asian options for assets driven by general Lévy processes using a change of numéraire and the characteristic triplet of the dual process. We apply the same technique to prove a similar relationship between floating...

We investigate a gravitational system in dimension one, started from some "uniform" random initial data. In Section 2, a connection is established with the additive coalescent. An hydrodynamic limit is obtained in Section 3 and it suggests a new construction of the standard additive coalescent....

We give a direct construction of a random measure which is equal in law to the collision local time between a catalytic super-Brownian motion and its catalytic measure. Under a regularity assumption on the catalytic measure, we show that the catalytic super-Brownian motion can be constructed...

We consider the Russian option introduced by Shepp and Shiryayev (Ann. Appl. Probab. 3 (1993) 631, Theory Probab. Appl. 39 (1995) 103) but with finite expiry and show that its space-time value function characterizes the unique solution to a free boundary problem. Further, using a method of...

We define a reinforced stochastic process of random variables indexed by the vertices of a k-tree and with values in a Polish space. The work presents a natural extension from an exchangeable to a partially exchangeable setting of previous work done by the authors.