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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 characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of stationarily local integrability plays a key role.
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
Using <M^c>, jump measure \mu and its compensator \nu we characterize the event where the stochastic exponential E(M) equals to zero.
A new definition of a multi-valued logarithm on time scales is introduced for delta-differentiable functions that never vanish. This new logarithm arises naturally from the definition of the cylinder transformation that is also at the heart…
We consider stochastic versions of the Cauchy exponential functional equation and give a martingale characterization of the general solution.
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and they are compared to…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
A stochastic Lie system on a manifold $M$ is a stochastic differential equation whose dynamics is described by a linear combination with functions depending on $\mathbb{R}^\ell$-valued semi-martigales of vector fields on $M$ spanning a…
Randomness in the sense of Martin-L\"of can be defined in terms of lower semicomputable supermartingales. We show that such a supermartingale cannot be replaced by a pair of supermartingales that bet only on the even bits (the first one)…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
Stochastic Network Calculus is a probabilistic method to compute performance bounds in networks, such as end-to-end delays. It relies on the analysis of stochastic processes using formalism of (Deterministic) Network Calculus. However,…
The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…
This chapter is divided into two parts. The first is largely expository and builds on Karandikar's axiomatisation of It{\^o} calculus for matrix-valued semimartin-gales. Its aim is to unfold in detail the algebraic structures implied for…
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified version. Our main…
Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…