In this paper we study Jensen’s inequality under quadratic g-expectation, i.e., the expectation generated by backward stochastic differential equations (BSDEs) with generator of quadratic growth in its component z. In particular, we define a new kind of convexity, the C-convexity, via a second...

We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the driver is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore, this forward process is reflected in a convex subset...

We discuss the construction and approximation of solutions to a nonlinear McKean–Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of neurons which interact with one another. Each time a...

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the functional limit theorems previously established in the...

This article is concerned with the study of fractal properties of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on R4 introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space H2(R4). We can...

We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behavior for large K, where K scales the population size. We focus on two loci: one under selection and one neutral. We distinguish...

We focus on the stationary distribution of a multidimensional semimartingale reflecting Brownian motion (SRBM) on a nonnegative orthant. Assuming that the stationary distribution exists and is decomposable—equal to the product of two marginal distributions, we prove that these marginal...

We prove the existence and uniqueness of solutions of reflected backward stochastic differential equations in time-dependent adapted and càdlàg convex regions D={Dt;t∈[0,T]}. We also show that the solution may be approximated by solutions of backward equations with reflection in...

We suggest three superpositions of COGARCH (sup-CO-GARCH) volatility processes driven by Lévy processes or Lévy bases. We investigate second-order properties, jump behaviour, and prove that they exhibit Pareto-like tails. Corresponding price processes are defined and studied. We find that the...

Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main result is convergence to a new continuum process, in...