We prove Hölder regularity for a general class of parabolic integro-differential equations,
which (strictly) includes many previous results. We present a proof that avoids the use of a …

Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time
fractional derivatives of order less than one are considered in the framework of viscosity …

This paper is concerned with the existence of viscosity solutions of nonlocal fully nonlinear
equations that are not translation-invariant. We construct a discontinuous viscosity solution …

We establish Hölder estimates for the time derivative of solutions of nonlocal parabolic
equations under mild assumptions for the boundary data. As a consequence we are able to …

This paper is concerned with existence of a C^ α C α viscosity solution of a second order
non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such …

In this article we consider a class of nonlinear integro-differential equations of the form in,
where,. The above equation appears in the study of ergodic control problems in when the …

We prove new comparison principles for viscosity solutions of nonlinear integro-differential
equations. The operators to which the method applies include but are not limited to those of …

We obtain the comparison principle for discontinuous viscosity sub-and supersolutions of
nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The …

In this paper, we consider the problem of minimizing the ruin probability of an insurance
company in which the surplus process follows the Sparre Andersen model. We recast this …

In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB)
equations, associated to nonlocal operators of integro-differential type. We consider the …