Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

Let $$\{\mu _{t}^{(i)}\}_{t\ge 0}$$ ( $$i=1,2$$ ) be continuous convolution semigroups (c.c.s.) of probability measures on $$\mathbf{Aff(1)}$$ (the affine group on the real line). Suppose that $$\mu _{1}^{(1)}=\mu _{1}^{(2)}$$ . Assume furthermore that $$\{\mu _{t}^{(1)}\}_{t\ge 0}$$ is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then $$\mu _{t}^{(1)}=\mu _{t}^{(2)}$$ for all $$t\ge 0$$ . We end up with a possible application in mathematical financ

Uniqueness of Embedding into a Gaussian Semigroup and a Poisson Semigroup with Determinate Jump Law ona Simply Connected Nilpotent Lie Group

Let {μ t (i) } t≥0 (i=1,2) be continuous convolution semigroups (c.c.s.) on a simply connected nilpotent Lie group G. Suppose that μ 1 (1) =μ 1 (2) . Assume furthermore that one of the following two conditions holds: (i) The c.c.s. {μ t (1) } t≥0 is a Gaussian semigroup (in the sense that its generating distribution just consists of a primitive distribution and a second-order differential operator) (ii) The c.c.s. {μ t (i) } t≥0 (i=1,2) are both Poisson semigroups, and the jump measure of {μ t (1) } t≥0 is determinate (i.e., it possesses all absolute moments, and there is no other nonnegative bounded measure with the same moments). Then μ t (1) =μ t (2) for all t≥0. As a complement, we show how our approach can be directly used to give anindependent proof of Pap's result on the uniqueness of the embedding Gaussian semigroup on simply connected nilpotent Lie groups. In this sense, our proof for the uniqueness of the embedding semigroup among all c.c.s. of a Gaussian measure can be formulated self-containe

Notiz zur Umlagerung von 5-Chloro-5-(dialkylamino)-pentadienalen

Similarly to 3-chloro-3-(dimethylamino)acrolein (2), 5-chloro-5-(dimethylamino)penta-2,4-dienal (6) easily rearranges in the presence of traces of acid to 2-(dimethylamino)pyrilium chloride (8), which is the postulated intermediate of the rearrangement of 6 to 5-chloropenta-2,4-dien-N,N-dimethylamide (10)

Synthese von 5-(Dialkylamino)-5-X-pentadienalen aus 'Push-Pull'-Eninen

5-Aminopent-2-ene-4-inals 1 are easily available by Pd(0)-catalyzed coupling of stannyl ynamines 6 or silyl ynamines 7 with 3-iodoacroleine. They react nearly quantitatively with acids like HCl or AcOH to give 5-amino-5-X-pentadienals 2, which are of interest in view of a postulated rearrangement

Phase Retrieval for Probability Distributions on Quantum Groups and Braided Groups

For nilpotent quantum groups [as introduced by Franz et al. (7)], we show that (in sharp contrast to the classical case) the symmetrization $$\mu * \bar \mu$$ of a probability distribution μ and the first moments of μ together determine uniquely the original distribution

Review on Experimental and Theoretical Investigations of Ultra-Short Pulsed Laser Ablation of Metals with Burst Pulses

Laser processing with ultra-short double pulses has gained attraction since the beginning of the 2000s. In the last decade, pulse bursts consisting of multiple pulses with a delay of several 10 ns and less found their way into the area of micromachining of metals, opening up completely new process regimes and allowing an increase in the structuring rates and surface quality of machined samples. Several physical effects such as shielding or re-deposition of material have led to a new understanding of the related machining strategies and processing regimes. Results of both experimental and numerical investigations are placed into context for different time scales during laser processing. This review is dedicated to the fundamental physical phenomena taking place during burst processing and their respective effects on machining results of metals in the ultra-short pulse regime for delays ranging from several 100 fs to several microseconds. Furthermore, technical applications based on these effects are reviewed

Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

Let {mu((i))(t)}(t >= 0) (i = 1, 2) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that mu((1))(1) = mu((2))(1). Assume furthermore that {mu((1))(t)}(t >= 0) is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then mu((1))(1) = mu((2))(1) for all t >= 0. We end up with a possible application in mathematical finance

Trickle bed co-processing of yellow greases and pyrolytic lignin

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