The martingale representation theorem in a Brownian filtration represents any square integrable r.v. ξ as a stochastic integral with respect to the Brownian motion. This is the simplest Backward SDE with nul generator and final data ξ, which can be seen as the non-Markov counterpart of the Cauchy problem in second order parabolic PDEs. Similarly, the notion of Second order BSDEs is the non-Mark...

A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

Let K/F be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky’s classification asserts that generic representations are parabolically induced from quasi-squareintegrable representations. We show, following a method developed by Cogdell and PiatetskiShapiro, that expected equality of the Rankin-Selberg type Asai L-function of a generic representation of GL(n, K), and the Asai L-fun...

The aim is to approve the Central limit theorem on MV-algebras by the new approach, presented by Riečan in [1]. We use the observable as a distribution function instead of the σ-homomorphism. The main idea is in local representation of σ-algebras. The following theorem is proved: Let M be a σ-complete MV-algebra with product, m : M −→ 〈0, 1〉 be a σadditive state, (xn)n be a sequence of independ...

Using positive semidefinite processes of Ornstein-Uhlenbeck type a multivariate Ornstein-Uhlenbeck (OU) type stochastic volatility model is introduced. We derive many important statistical and probabilistic properties, e.g. the complete second order structure and a state-space representation. Noteworthy, many of our results are shown to be valid for the more general class of multivariate stocha...

Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(XT ), f being the Fourier transform of a finite measure μ, we provide explicit Kunita-Watanabe and Föllmer-Schweizer decompositions. The representation is expressed by means of two significant maps: the expectation and derivative operators related to the characteristics...

• Decomposition by central characters • Square-integrable cuspforms • Smoothness of cuspforms • Eigen-cuspforms and automorphic representation • Dirichlet series versus zeta and L-functions • L-functions defined via local data • Factoring unitary representations of adele groups • Spherical representations and Satake parameters • Local data, L-groups, higher L-functions References and historical...

Let Sp(n,R) be the symplectic group, and K∗ n its maximal compact subgroup. Then G = Sp(n,R)/K∗ n can be realized as the Siegel domain of type one. The square-integrable representation of G gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent s...