Related papers: How badly are the Burholder-Davis-Gundy inequaliti…
Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some…
We present a new proof of the Burkholder-Davis-Gundy inequalities for $1\leq p<\infty$. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a…
{Consider a c\`adl\`ag local martingale $M$ with square brackets $[M]$. In this paper, we provide upper and lower bounds for expectations of the type ${\mathbb E} [M]^{q/2}_{\tau}$, for any stopping time $\tau$ and $q\ge 2$, in terms of…
Two concepts of random stopping times in continuous time have been defined in the literature, mixed stopping times and randomized stopping times. We show that under weak conditions these two concepts are equivalent, and, in fact, that all…
We present several applications of the pathwise Burkholder-Davis-Gundy (BDG) inequalities. Most importantly we prove them for cadlag semimartingales and a general function $\Phi$, and use this to derive BDG inequalities (non-pathwise ones)…
We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures.
Recently, D. Williams \cite{williams} gave an explicit example of a random time $\rho $ associated with Brownian motion such that $\rho $ is not a stopping time but $\mathbb{E}M_{\rho}=\mathbb{E}M_{0}$ for every bounded martingale $M$. The…
We propose a geometric approach for bounding average stopping times for stopped random walks in discrete and continuous time. We consider stopping times in the hyperspace of time indexes and stochastic processes. Our techniques relies on…
By taking into account that all real measurements are performed successively, during time, it is concluded that the violation of the Bell's inequalities in the Nature does not refute (even in an ideally perfect experiment) the theories…
According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Recent research has shown that, combined with quantum theory, this…
Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…
Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…
We prove an inequality for the spectral norm of matrix valued stochastic integrals. This inequality can be seen either as a non-commutative version of the Burkholder-Davis-Gundy inequality or as an extension of the non-commutative…
The aim of this note is to give some Burkholder-Davis-Gundy type inequalities which are valid for the Ito stochastic integral with respect to Banach valued Levy noise.
This paper analyzes effects of time-dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non-coincidence [and hence whether or not a pair contributes to the actual data] is controlled by…
In this paper, we introduce a new method for study on backward stochastic differential equations with stopping time as time horizon. And using this, we show that some results on backward stochastic differential equations with constant time…
Employing an arbitrary velocity gauge transformation this contribution argues that the breaking of time symmetry is a natural consequence of irreversibility.
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at…
This paper quantifies the interplay between the non-arbitrage notion of No-Unbounded-Profit-with-Bounded-Risk (NUPBR hereafter) and additional information generated by a random time. This study complements the one of…
We give a proof of the maximal inequalities of Burkholder, Davis and Gundy for real as well as Hilbert-space-valued local martingales using almost only stochastic calculus. Some parts of the exposition, especially in the infinite…