相关论文: Variational representations of Varadhan Functional…

In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The…

Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational…

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…

We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…

Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…

We associate motivic zeta functions to a large class of infinite dimensional Lie algebras

We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of the space of Young measures. We will show that in the space…

We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and…

We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory…

We consider two non-linear generalizations of fractal interpolating functions generated from iterated function systems. The first corresponds to fitting data using a Kth-order polynomial, while the second relates to the freedom of adding…

In this paper the theory of 2-Variable Boolean Operation (2-VBO) has been discussed on a pair of n-bit strings. 2-VBO serves to bring out the relation between numbers which when plot on a 2-D surface form interesting patterns; patterns that…

The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…

The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…

We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…

Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…

In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…

We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma…