On the random version of Ważewski theorem
On the regularity of many-particle dynamical systems perturbed by white noise.
On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model
We study the pathwise regularity of the map φ↦I(φ)=∫0T〈φ(Xt), dXt〉, where φ is a vector function on ℝd belonging to some Banach space V, X is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of V will be called stochastic current. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture...
On the representation of solutions of stochastic differential equations
On the short time asymptotic of the stochastic Allen–Cahn equation
A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.
On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...
On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.
On the smallest eigenvalue of the Stokes operator in a domain with fine-grained random boundary.
On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions.
On the stability of cubic mappings and quadratic mappings in random normed spaces.
On the stability of stationary solutions of a linear integro-differential equation.
On the stabilization of the energy of a harmonic oscillator disturbed by random processes of the “white and shot noises” types.
On the stochastic regularity of sequence transformations operating in a Banach space
On the strong convergence to equilibrium for randomly perturbed dynamical systems
On the unique solvability of some nonlinear stochastic PDEs.
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions
On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
In [Probab. Theory Related Fields141 (2008) 543–567], the authors proved the uniqueness among the solutions of quadratic BSDEs with convex generators and unbounded terminal conditions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman–Kac formula proved...
On the variance of the number of real roots of a random trigonometric polynomial.
On transformations of Wiener space.
On two transfer principles in stochastic differential geometry