Let Zt,z[nu] be a -valued mixed diffusion process controlled by [nu] with initial condition Zt,z[nu](t)=z. In this paper, we characterize the set of initial conditions such that Zt,z[nu] can be driven above a given stochastic target at time T by proving that the corresponding value function is a...

We consider the integral equation driven by a standard Brownian motion and fractional Brownian motion (fBm). Since fBm is not a semimartingale, we cannot use the semimartingale theory to define an integral with respect to the fBm. Furthermore, a well-developed theory of stochastic differential...

We study the solution X={Xt}t[set membership, variant][0,T] to a Poisson-driven SDE. This equation is "irregular" in the sense that one of its coefficients contains an indicator function, which allows to generalize the usual situations: the rate of jump of X may depend on X itself. For t0 fixed,...

Backward stochastic Riccati equations are motivated by the solution of general linear quadratic optimal stochastic control problems with random coefficients, and the solution has been open in the general case. One distinguishing difficult feature is that the drift contains a quadratic term of...

We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and perimeter-interacting point processes (with stochastic grains), invariant...

Backward stochastic differential equations (BSDE) also gives the weak solution of a semi-linear system of parabolic PDEs with a second-order divergence-form partial differential operator and possibly discontinuous coefficients. This is proved here by approximation. After that, a homogenization...

We consider the hydrodynamic limit for a certain Brownian directed percolation model, and establish uniform concentration results. In view of recent work on the connection between this directed percolation model and eigenvalues of random matrices, our results can also be interpreted as uniform...

Let [tau](x)=inf{t0: Q(t)[greater-or-equal, slanted]x} be the time of first overflow of a queueing process {Q(t)} over level x (the buffer size) and . Assuming that {Q(t)} is the reflected version of a Lévy process {X(t)} or a Markov additive process, we study a variety of algorithms for...

In the study of quasi-birth-and-death (QBD) processes, the first passage probabilities from states in level one to the boundary level zero are of fundamental importance. These probabilities are organized into a matrix, usually denoted by G. The matrix G is the minimal nonnegative solution of a...

In this paper, we obtain a sharpening of the functional modulus of continuity and large increments in terms of (r,p)-capacities on the Wiener space.