Related papers: Fitting Martingales To Given Marginals

We develop a general approach of the almost sure central limit theorem for the quasi-continuous vectorial martingales and we release a quadratic extension of this theorem while specifying speeds of convergence. As an application of this…

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when…

In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…

In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and…

We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions…

We give a necessary and sufficient condition on a sequence of functions on a set $\Omega$ under which there is a measure on $\Omega$ which renders the given sequence of functions a martingale. Further such a measure is unique if we impose a…

Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…

When the \textit{martingale representation property} holds, we call any local martingale which realizes the representation a \textit{representation process}. There are two properties of the \textit{representation process} which can greatly…

We give a new characterization for mutual absolute continuity of probability measures on a filtered space. For this, we introduce a martingale limit $M$ that measures the similarity between the tails of the probability measures restricted…

We consider SDEs with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness.We then…

We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the…

We prove a new inequality controlling the large deviations of the empirical measure of a Markov chain. This inequality is based on the martingale used by Donsker and Varadhan and the minimax theorem. It holds for convex sets and it requires…

We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…

We prove that for a so-called sticky process $S$ there exists an equivalent probability $Q$ and a $Q$-martingale $\tilde{S}$ that is arbitrarily close to $S$ in $L^p(Q)$ norm. For continuous $S$, $\tilde{S}$ can be chosen arbitrarily close…

This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…

This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…

Let $A$ be a pseudo-differential operator with symbol $q(x,\xi)$. In this paper we derive sufficient conditions which ensure the existence of a solution to the $(A,C_c^{\infty}(\mathbb{R}^d))$-martingale problem. If the symbol $q$ depends…