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We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (X t) t ∈ [ 0 , T ] and a jump-diffusion process (X t ∗) t ∈ [ 0 , T ] . Our bounds are expressed using the stochastic characteristics of (X t) t ∈ [ 0 , T ] and the jump-diffusion coefficients of (X t ∗) t ∈ [ 0 , T ] evaluated in X t , and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and L p integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation. [ABSTRACT FROM AUTHOR]

Bernstein processes over a finite time interval are simultaneously forward and backward Markov processes with arbitrarily fixed initial and terminal probability distributions. In this paper, a large deviation principle is proved for a family of Bernstein processes (depending on a small parameter ħ which is called the Planck constant) arising naturally in Euclidean quantum physics. The method consists in nontrivial Girsanov transformations of integral forms, suitable equivalence forms for large deviations and the (local and global) estimates on the parabolic kernel of the Schrödinger operator. [ABSTRACT FROM AUTHOR]

We derive joint factorial moment identities for point processes with Papangelou intensities. Our proof simplifies previous combinatorial approaches to the computation of moments for point processes. We also obtain new explicit sufficient conditions for the distributional invariance of point processes with Papangelou intensities under random transformations. [ABSTRACT FROM AUTHOR]