Related papers: Minimal $f^q$-martingale measures for exponential …
Let $\mathbb{\hat{E}}$ be the upper expectation of a weakly compact but non-dominated family $\mathcal{P}$ of probability measures. Assume that $Y$ is a $d$-dimensional $\mathcal{P}$-semimartingale under $\mathbb{\hat{E}}$. Given an open…
There is a natural connection between the class of diffusions, and a certain class of solutions to the Skorokhod Embedding Problem (SEP). We show that the important concept of minimality in the SEP leads to the new and useful concept of a…
We extend an inequality of Merryfield, valid in the continuous setting, to discrete multiparameter martingales. As a consequence, we obtain the $L^p$ comparison of the maximal function with the square function: \begin{align*} E[(Sf)^p]…
A function $f=f_T$ is called least energy approximation to a function $B$ on the interval $[0,T]$ with penalty $Q$ if it solves the variational problem $$ \int_0^T \left[ f'(t)^2 + Q(f(t)-B(t)) \right] dt \searrow \min. $$ For quadratic…
We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and…
We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local projective measurement on the qubit, which is valid for general entropic forms and becomes exact in…
The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical…
Let $p_t(x)$, $f_t(x)$ and $q_t^*(x)$ be the densities at time $t$ of a real L\'evy process, its running supremum and the entrance law of the reflected excursions at the infimum. We provide relationships between the asymptotic behaviour of…
We give simple proofs that for a continuous local martingale M_t: 1) \liminf_{\epsilon->0} \epsilon \log Ee^{(1-\epsilon) <M>_\infty /2} < \infty ==> E\exp(M_\infty - <M>_\infty /2) = 1, 2) \liminf_{\epsilon->0} \epsilon \log\sup_{t>=0}…
Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that…
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential L\'evy processes…
Given an n-dimensional stochastic process X driven by P-Brownian motions and Poisson random measures, we seek the probability measure Q, with minimal relative entropy to P, such that the Q-expectations of some terminal and running costs are…
In this article we relate the set of structure preserving equivalent martingale measures $(\mathcal{M})$ for financial models driven by semimartingales with conditionally independent increments to a set of measurable and integrable…
It is known that the heuristic principle, referred to as the multifractal formalism, need not hold for self-similar measures with overlap, such as the $3$-fold convolution of the Cantor measure and certain Bernoulli convolutions. In this…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
Understanding and classifying multipartite entanglement is fundamental to quantum information processing. This work focuses on absolutely maximally entangled (AME) states, a class of highly entangled states characterized by their maximal…
Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…
We study class of L\'{e}vy processes having distributions being indentifiable by moments. We define system of polynomial martingales \newline $\left\{ M_{n}(X_{t},t),\mathcal{F}_{\leq t}\right\} _{n\geq 1},$ where $% \mathcal{F}_{\leq t}$…
We provide a criterion for establishing lower bounds on the rate of convergence in $f$-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…