相关论文: A martingale bound for the entropy associated with…

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…

This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685--712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done…

We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…

We show how to determine the maximum and minimum possible values of one measure of entropy for a given value of another measure of entropy. These maximum and minimum values are obtained for two standard forms of probability distribution (or…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of $d$-dimensional bounded monotonic functions under $L^p$ norms. It is interesting to see that both the metric entropy and bracketing entropy…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

We introduce a concept of dissipative measure valued martingale solutions for stochastic compressible Navier-Stokes equations. These solutions are weak from a probabilistic perspective, since they include both the driving Wiener process and…

For a $d$-dimensional stochastic process $(S_n)_{n=0}^N$ we obtain criteria for the existence of an equivalent martingale measure, whose density $z$, up to a normalizing constant, is bounded from below by a given random variable $f$. We…

We study a martingale Schr\"odinger bridge problem: given two probability distributions, find their martingale coupling with minimal relative entropy. Our main result provides Schr\"odinger potentials for this coupling. Namely, under…

We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.e., the probability space and the driving Wiener process are…

We study the joint laws of a continuous, uniformly integrable martingale, its maximum, and its minimum. In particular, we give explicit martingale inequalities which provide upper and lower bounds on the joint exit probabilities of a…

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…

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have…

We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…

We prove an estimate for weighted $p$-th moments of the pathwise $r$-variation of a martingale in terms of the $A_{p}$ characteristic of the weight. The novelty of the proof is that we avoid real interpolation techniques.

In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively…