In Gapeev and Kühn (2005) [8], the Dynkin game corresponding to perpetual convertible bonds was considered, when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but driven by a spectrally positive Lévy process. We...

In this article we prove that stochastic differential equation (SDE) with Sobolev drift on a compact Riemannian manifold admits a unique [nu]-almost everywhere stochastic invertible flow, where [nu] is the Riemannian measure, which is quasi-invariant with respect to [nu]. In particular, we...

We derive a satisfying rate of convergence of the Marcus-Lushnikov process towards the solution to Smoluchowski's coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in (-[infinity],1]. It relies on the use of a...

We develop an idea of Evans and O'Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called 'backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical...

Multivariate random fields whose distributions are invariant under operator-scalings in both the time domain and the state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are characterized. Two classes of operator-self-similar...

Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding Lévy measure and the Lévy-Khinchin exponent.

We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional...

In this paper, we consider the Stratonovich reflected SDE in a bounded domain . Letting be the N-dyadic piecewise linear interpolation of Wt, we show that the distribution of the solution to the reflected ODE converges weakly to that of (Xt,Lt). Hence, we prove a distributional version for...

We provide asymptotic results for time-changed Lévy processes sampled at random instants. The sampling times are given by the first hitting times of symmetric barriers, whose distance with respect to the starting point is equal to [epsilon]. For a wide class of Lévy processes, we introduce a...