We show that a Markov process in a manifold invariant under the action of a compact Lie group K induces a Lévy process in each K-orbit by "forcing" it to run in the orbit.

We construct a class of interactive measure-valued diffusions driven by a historical super-Brownian motion and an independent white noise by solving a certain stochastic equation. In doing so, we show that the approach of Perkins (2002) [3] can be used to study the problem examined by Dawson...

The backward two-dimensional stochastic Navier-Stokes equations (BSNSEs, for short) with suitable perturbations are studied in this paper, over bounded domains for incompressible fluid flow. A priori estimates for adapted solutions of the BSNSEs are obtained which reveal a pathwise...

In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [A. Ayache, F. Roueff, Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C.R. Acad. Sci. Paris Ser. I. 344 (6) (2007)...

We consider a random variable X satisfying almost-sure conditions involving G:=<DX,-DL-1X> where DX is X's Malliavin derivative and L-1 is the pseudo-inverse of the generator of the Ornstein-Uhlenbeck semigroup. A lower- (resp. upper-) bound condition on G is proved to imply a Gaussian-type lower (resp....</dx,-dl-1x>

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter [tau]. The evolution is by independent updating of the underlying Bernoulli...

We consider a new class of estimators for volatility functionals in the setting of frequently observed Ito diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of...

We investigate integral functionals , t=0, where m is a nonnegative measure on and LY is the local time of a Wiener process with drift, i.e., Yt=Wt+t, t=0, with a standard Wiener process W. We give conditions for a.s. convergence and divergence of Tt, t=0, and T[infinity]. In the second part...

Isotropic Brownian flows (IBFs) are a fairly natural class of stochastic flows which has been studied extensively by various authors. Their rich structure allows for explicit calculations in several situations and makes them a natural object to start with if one wants to study more general...

We present a general framework for solving stochastic porous medium equations and stochastic Navier-Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion...