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1.
We prove that on simply connected step 2-nilpotent Lie groupsG any limit of a commutative infinitesimals triangular system of probability measures which are either all symmetric or supported by some discrete subgroupH is infinitely divisible onG resp.H.  相似文献   

2.
The Prokhorov-Loève strong law of large numbers is carried over to countable subgroups of simply connected step 2-nilpotent Lie groups. Proceedings of the Seminar on Stability, Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part, II.  相似文献   

3.
s-stable laws on Hilbert spaces, associated with some nonlinear transformations, were introduced by Jurek.(16, 18) Here, we interpret certain s-stable motions as limits of total amount of claims processes (up to a deterministic reserve) of a portfolio of (nontraded) excess-of-loss reinsurance contracts and show that they lead to Erlang's model. We also give explicit formulas for the price of perpetual American options in case the logarithm of the price of the underlying asset is an s-stable motion. Furthermore, we generalize the concept of s-stability to simply connected nilpotent Lie groups. For step 2-nilpotent Lie groups we characterize the Lévy measure and the s-domain of attraction of nongaussian s-stable convolution semigroups.  相似文献   

4.
A limit theorem due to J. Kuelbs and M. Ledoux, valid for dilatation-stable laws on type 2-Banach spaces, is carried over to stable laws on simply connected step 2-nilpotent Lie groupsG. We show that for products of i.i.d. random variables in the of attraction of a nondegenerate semigroup onG, where is a one-parameter automorphism group acting contracting onG, a certain intermediate trimming procedure, together with a suitable norming, always yields a nondegenerate centered Gaussian limit.  相似文献   

5.
Agota Figula 《代数通讯》2013,41(1):444-468
We prove that each 3-dimensional connected topological loop L having a solvable Lie group of dimension ≤5 as the multiplication group of L is centrally nilpotent of class 2. Moreover, we classify the solvable non-nilpotent Lie groups G which are multiplication groups for 3-dimensional simply connected topological loops L and dim G ≤ 5. These groups are direct products of proper connected Lie groups and have dimension 5. We find also the inner mapping groups of L.  相似文献   

6.
A law of iterated logarithm (LIL) in small time and an asymptotic estimate of modulus of continuity are proved for Brownian motion on the loop group ?(G) over a compact connected Lie group G. Upper bounds are obtained via infinite-dimensional deviation inequalities for functionals on the path space ?(?(G)) on ?(G), such as the supremum of Brownian motion on ?(G), which are proved from the Clark–Ocone formula on ?(?(G)). The lower bounds rely on analog finite-dimensional results that are proved separately on Riemannian path space.  相似文献   

7.
We prove that, in some situations, an induced action from a normal subgroup preserves a geometric structure. Combined with known geometric rigidity results, this result implies certain rigidity statements concerning the full diffeomorphism group of a manifold. It also provides many examples of actions on Lorentz manifolds. Combining these with a small number of well-known actions, we get the full list of connected, simply connected Lie groups admitting a locally faithful, orbit nonproper action by isometries of a connected Lorentz manifold. We give an example of a connected nilpotent Lie group with no complicated action on a Lorentz manifold. We show that, if a connected Lie group has a normal closed subgroup isomorphic to a (two-dimensional) cylinder, then it admits a locally faithful, orbit nonproper action by isometries of a connected Lorentz manifold.  相似文献   

8.
We study a decomposition of a general Markov process in a manifold invariant under a Lie group action into a radial part (transversal to orbits) and an angular part (along an orbit). We show that given a radial path, the conditioned angular part is a nonhomogeneous Lévy process in a homogeneous space, we obtain a representation of such processes and, as a consequence, we extend the well-known skew-product of Euclidean Brownian motion to a general setting.   相似文献   

9.
In this paper we prove existence and regularity results for a class of semilinear evolution equations that are satisfied by vector potentials associated with Maxwell’s equations in Carnot groups (connected, simply connected, stratified nilpotent Lie groups). The natural setting for these equations is provided by the so-called Rumin’s complex of intrinsic differential forms.  相似文献   

10.
We give a proof of the Plancherel formula for real almost algebraic groups in the philosophy of the orbit method, following the lines of the one given by M. Duflo and M. Vergne for simply connected semisimple Lie groups. Main ingredients are: (1) Harish-Chandra's descent method which, interpreting Plancherel formula as an equality of semi-invariant generalized functions, allows one to reduce it to a neighbourhood of zero in the Lie algebra of the centralizer of any elliptic element; (2) character formula for representations constructed by M. Duflo, we recently proved; (3) Poisson-Plancherel formula near elliptic elements s in good position, a generalization of the classical Poisson summation formula expressing the Fourier transform of the sum of a series of Harish-Chandra type elliptic orbital integrals in the Lie algebra centralizing s as a generalized function supported on a set of admissible regular forms in the dual of this Lie algebra.  相似文献   

11.
We prove large and moderate deviation estimates for products of i.i.d. r.v.'s taking values on simply connected nilpotent Lie groups as a consequence of large and moderate deviation results for stochastic processes which are solutions of O.D.E. with random coefficients.  相似文献   

12.
《代数通讯》2013,41(12):5439-5463
The explicit formula for the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group is obtained. In particular, we prove that a function f: NR can be realized (up to equivalence) as the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group if and only if fnr for some nonnegative rQ. Considering lattices in Lie groups, we establish the analogous results for finitely generated nilpotent groups.  相似文献   

13.
The Brownian rough path is the canonical lifting of Brownian motion to the free nilpotent Lie group of order 2: Equivalently, it is a process taking values in the algebra of Lie polynomials of degree 2, which is described explicitly by the Brownian motion coupled with its area process. The aim of this article is to compute the finite dimensional characteristic functions of the Brownian rough path in ?d and obtain an explicit formula for the case when d = 2  相似文献   

14.
We study the density of closed geodesics property on 2-step nilmanifolds Γ\N, where N is a simply connected 2-step nilpotent Lie group with a left invariant Riemannian metric and Lie algebra ?, and Γ is a lattice in N. We show the density of closedgeodesics property holds for quotients of singular, simply connected, 2-step nilpotent Lie groups N which are constructed using irreducible representations of the compact Lie group SU(2). Received: 8 November 2000 / Revised version: 9 April 2001  相似文献   

15.
We characterize the left-invariant Riemannian metrics on each of the six unimodular simply connected 3-dimensional Lie groups which give rise to 3-, 4-, or 6-dimensional isometry groups. It turns out that this classification is independent of curvature properties.  相似文献   

16.
We generalize the classical Paley–Wiener theorem to special types of connected, simply connected, nilpotent Lie groups: First we consider nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. Then we consider nilpotent Lie groups such that the co-adjoint orbits of all the elements of a dense subset of the dual of the Lie algebra 𝔤* are flat (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

17.
The infinitesimal generators of Lévy processes in Euclidean space are pseudodifferential operators with symbols given by the Lévy-Khintchine formula. This classical analysis relies heavily on Fourier analysis which, in the case when the state space is a Lie group, becomes much more subtle. Still the notion of pseudo-differential operators can be extended to connected, simply connected nilpotent Lie groups by employing the Weyl functional calculus. With respect to this definition, the generators of Lévy processes in the simplest step 3 nilpotent Lie group G are pseudodifferential operators which admit C c (G) as its core.  相似文献   

18.
A new definition of an admitted Lie group of transformations for stochastic differential equations involving Brownian motion is presented. The transformation of the dependent variables involves time as well, and it is proved that Brownian motion is transformed to Brownian motion. Applications to a variety of stochastic differential equations are presented.  相似文献   

19.
We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.  相似文献   

20.
 In this paper we give a characterization of those reductive or solvable connected, not necessarily simply connected, Lie groups which permit a non-degenerate group order. A non-degenerate group ordering on G always defines a pointed generating invariant convex cone W in the Lie algebra of G, but not every such cone arises in this way. The cones that do are called global. To decide whether a given cone is global or not is a difficult problem which for simply connected groups and invariant cones has completely been solved by Gichev.  相似文献   

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