Related papers: Martingale-Coboundary Representation for a Class o…
As a continuation of [GasparPopa] this paper treats the stationary and stationarily cross-correlated multivariate stochastic mappings. Moreover for the case of multivariate random distribution fields, a particular form for the operator…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
We study representations of a random variable $\xi$ as an integral of an adapted process with respect to the Lebesgue measure. The existence of such representations in two different regularity classes is characterized in terms of the…
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…
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…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
In this paper we explore the fundamentals of the Martingale Representation Theorem (MRT) and a closely related result, the Clark-Ocone formula. We also investigate how far these theorems can be taken, notably beyond the regular Sobolev…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these…
A general proposition is proved relating multiplicities (of restriction of a representation of a group to a subgroup) under basechange, and used to calculate some multiplicities for cuspidal representations which become principal series…
This paper considers the nonlinear theory of G-martingales as introduced by Peng. A martingale representation theorem for this theory is proved by using the techniques and the results established in an accompanying paper for the second…
A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…
The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
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 {\em stochastic maximal inequality} derived by using the formula for…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…