A measure-valued process describes the evolution of a population that evolves according to
the law of chance. In this chapter we provide some basic characterizations and constructions …

This paper considers multidimensional jump type stochastic differential equations with super
linear and non-Lipschitz coefficients. After establishing a sufficient condition for …

In this paper, we consider the Heston-CIR model with Lévy process for pricing in the foreign
exchange (FX) market by providing a new formula that better fits the distribution of prices. To …

arXiv:1403.0245v2 [math.PR] 10 Feb 2015 Page 1 arXiv:1403.0245v2 [math.PR] 10 Feb 2015
Stochastic differential equation with jumps for multi-type continuous state and continuous time …

This work is devoted to the study of conservative affine processes on the canonical state
space D=R_+^m*R^n, where m+n>0. We show that each affine process can be obtained as …

In this paper, we study mean-field stochastic differential equations with jumps. By Malliavin
calculus for Wiener–Poisson functionals, sharp gradient estimates are derived. Based on the …

We establish the exponential convergence with respect to the L 1-Wasserstein distance and
the total variation for the semigroup corresponding to the stochastic differential equation d X …

Coupling by reflection mixed with synchronous coupling is constructed for a class of
stochastic differential equations (SDEs) driven by Lévy noises. As an application, we …

We introduce a new Wright-Fisher type model for seed banks incorporating “simultaneous
switching”, which is motivated by recent work on microbial dormancy ([21],[28]). We show …

We consider SDEs driven by multiplicative pure jump Lévy noises, where Lévy processes
are not necessarily comparable to α-stable-like processes. By assuming that the SDE has a …