Stochastic integration and differential equations

TL;DR: In this paper, the basic theory for hyperfinite Levy processes was developed and a characterization in terms of transition probabilities was given. But the standard part of a hyperinite Levy process is a (standard) Levy process, and given a generating triplet (C, C, ) for standard Levy processes, we can construct hyper-fiend Levy processes whose standard parts corre- spond to this triplet.

TL;DR: In this paper, the authors considered the non-degenerate second-order parabolic partial differential equations of non-divergence form with bounded measurable coefficients and obtained the Gaussian bounds and the lower bound of the index of the H-older continuity with respect to the initial point.

TL;DR: In this paper, the central limit theorem for diffusion with finite speed measure is used to prove weak convergence of the local time density estimator and the empirical distribution function on the full state space.

TL;DR: In this article, the existence and uniqueness of the solution to neutral stochastic functional differential equation with infinite delay and Poisson jumps in the phase space B with non-Lipschitz coefficients was proved.