In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H[set membership, variant](1/3,1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process...

We study the -time regularity of the Z-component of a Markovian BSDE, whose terminal condition is a function g of a forward SDE (Xt)0=t=T. When g is Lipschitz continuous, Zhang (2004) [18] proved that the related squared -time regularity is of order one with respect to the size of the time mesh....

Itô's theory of excursion point processes is reviewed and the following topics are discussed: Application of the theory to one-dimensional diffusion processes on half-intervals satisfying Feller's boundary conditions, and its multi-dimensional extension, i.e., the application of the theory to...

We consider kernel density and regression estimation for a wide class of nonlinear time series models. Asymptotic normality and uniform rates of convergence of kernel estimators are established under mild regularity conditions. Our theory is developed under the new framework of predictive...

A joint large deviation principle for G-Brownian motion and its quadratic variation process is presented. The rate function is not a quadratic form due to quadratic variation uncertainty. A large deviation principle for stochastic differential equations driven by G-Brownian motion is also...

We study the object formally defined as where Xt denotes the symmetric stable processes of index 0[beta]=2 in Rd. When , this has to be defined as a limit, in the spirit of renormalized self-intersection local time. We obtain results about the large deviations and laws of the iterated logarithm...

Stochastic calculus and stochastic differential equations for Brownian motion were introduced by K. Itô in order to give a pathwise construction of diffusion processes. This calculus has deep connections with objects such as the Fock space and the Heisenberg canonical commutation relations,...

We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality (PVI) with a mixed nonlinear multivalued Neumann-Dirichlet boundary condition: where [not partial differential][phi] and [not partial differential][psi] are subdifferential operators and is a...

We present a general model for default times, making precise the role of the intensity process, and showing that this process allows for a knowledge of the conditional distribution of the default only "before the default". This lack of information is crucial while working in a multi-default...

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space Hn () under weaker assumptions than those used by X. Zhou [X. Zhou, A duality...