We introduce a forward scheme for simulating backward SDEs. Compared to existing schemes, ours avoids high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, depending on the time partition, is significantly...

In this paper we consider a class of mixed optimal control/optimal stopping problems related to the choice of the best time to sell a single unit of an indivisible asset. We assume that in addition to the indivisible asset, the agent has access to a financial market. Investments in the financial...

We consider the standard first-passage percolation in for d=2 and we denote by [phi]nd-1,h(n) the maximal flow through the cylinder ]0,n]d-1x]0,h(n)] from its bottom to its top. Kesten proved a law of large numbers for the maximal flow in dimension 3: under some assumptions, [phi]nd-1,h(n)/nd-1...

Consider the centred Gaussian field on the lattice , d large enough, with covariances given by the inverse of , where [Delta] is the discrete Laplacian and , the qj satisfying certain additional conditions. We extend a previously known result to show that the probability that all spins are...

Let l(n,x) be the local time of a random walk on . We prove a strong law of large numbers for the quantity for all [alpha]>=0. We use this result to describe the distribution of the local time of a typical point in the range of the random walk.

We consider a Bayesian-martingale approach to the general change-point detection problem. In our setting the change-point represents a random time of bifurcation of two probability measures given on the space of right-continuous functions. We derive a reflecting backward stochastic differential...

We derive and analyze Monte Carlo estimators of price sensitivities ("Greeks") for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A...

A path decomposition at the infimum for positive self-similar Markov processes (pssMp) is obtained. Next, several aspects of the conditioning to hit 0 of a pssMp are studied. Associated to a given pssMp X, that never hits 0, we construct a pssMp X[downwards arrow] that hits 0 in a finite time....

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular...

We define the Burgers superprocess to be the solution of the stochastic partial differential equation where t=0, , and W is space-time white noise. Taking [gamma]=0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking [lambda]=0 gives the...