An Itô–Stratonovich formula for Gaussian processes: A Riemann sums approach

An exact renormalization formula for Gaussian exponential sums and applications

Such sums have been the object of many studies (see e.g. [9, 6, 10, 13, 14]) and have applications in various fields of mathematics and physics. In the present paper, we prove a renormalization formula (see Theorem 2.1) analogous to the one first introduced in [9]. In our formula, the “remainder term” is given explicitly by a special function (see section 1). We use this renormalization formula...

Multidimensional Wick-itô Formula for Gaussian Processes

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

A Bayes Formula for Gaussian Noise Processes and its Applications

An elementary approach is used to derive a Bayes-type formula, extending the Kallianpur–Striebel formula for the nonlinear filters associated with the Gaussian noise processes. In the particular cases of certain Gaussian processes, recent results of Kunita and of Le Breton on fractional Brownian motion are derived. We also use the classical approximation of the Brownian motion by the Ornstein–U...

An Integral Riemann-roch Formula for Flat Line Bundles

Let p be a unitary representation of the subgroup K of the finite group 0, with inclusion map / . Then, if /, and /# denote the transfer maps for representation theory and cohomology respectively, Knopfmacher [8] has proved that, for all k ^ 1, there exist positive integers Mk such that Mk(k\chk(fiP))=U(Mkk\ohk(P)). Here ch& denotes the fcth component of the Chern character, so that k! chfc is ...