Covariant Mehler semigroups in Hilbert space

We find necessary and sufficient conditions for a generalised Mehler semigroup to be covariant under the action of a locally compact group. These are then applied to implement "noise reduction" for Hilbert-space valued Ornstein - Uhlenbeck processes driven by Levy processes

Wrong But Reasonable : The Fourth Amendment Particularity Requirement After United States v. Leon

This Note analyzes the application of the good-faith exception to search warrant particularity violations under the Fourth Amendment. The question compelled by United States v. Leon and Massachusetts v. Sheppard is when, if ever, a particularity-defective warrant will sustain an officer\u27s reasonable reliance.\u27\u27 The Note briefly discusses how particularity traditionally has been assessed under the fourth amendment. The author examines the Supreme Court\u27s holding in Massachusetts v. Sheppard, and contrasts several circuit court cases that have applied Sheppard\u27s objectively reasonable standard of good faith to warrants involving particularity defects. Finally, the Note concludes that the approach taken by the Second Circuit Court of Appeals in United States v. Buck is a preferable approach because it encourages courts to establish clearer standards for the particularity of warrants under the Fourth Amendment

Universal Malliavin calculus in Fock and Levy-Ito spaces

We review and extend Lindsay's work on abstract gradient and divergence operators in Fock space over a general complex Hilbert space. Precise expressions for the domains are given, the L2-equivalence of norms is proved and an abstract version of the It^o-Skorohod isometry is established. We then outline a new proof of It^o's chaos expansion of complex Levy-It^o space in terms of multiple Wiener-Levy integrals based on Brownian motion and a compensated Poisson random measure. The duality transform now identies Levy-It^o space as a Fock space. We can then easily obtain key properties of the gradient and divergence of a general Levy process. In particular we establish maximal domains of these operators and obtain the It^o-Skorohod isometry on its maximal domain

Extending stochastic resonance for neuron models to general Levy noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Levy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general Levy noise models. We achieve this by showing that �¿large jump�¿ discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a �¿forbidden intervals�¿ theorem as in Patel and Kosko's paper

Probability measures on compact groups which have square-integrable densities

We apply Peter–Weyl theory to obtain necessary and sufficient conditions for a probability measure on a compact group to have a square-integrable density. Applications are given to measures on the d-dimensional torus

CHALLENGES TO FOOD DISTRIBUTION RESEARCH IN THE 1970'S

The Speaker keynotes the problems for food distribution in the next decade, points out the problems and errors of the past and challenges the researchers to set about solving the problems of the future.Marketing,

Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality

We give a short summary of Varopoulos' generalised Hardy-Littlewood-Sobolev inequality for self-adjoint $C_{0}$ semigroups and give a new probabilistic representation of the classical fractional integral operators on $\R^n$ as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-Littlewood-Sobolev inequality based on Burkholder-Gundy and Doob's inequalities for martingales

Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space

We investigate a class of Hilbert space valued martingale-valued measures whose covariance structure is determined by a trace class positive operator valued measure. The paradigm example is the martingale part of a Levy process. We develop both weak and strong stochastic integration with respect to such martingale-valued measures. As an application, we investigate the stochastic convolution of a C0-semigroup with a Levy process and the associated Ornstein-Uhlenbeck process. We give an in¯nite dimensional generalisation of the concept of operator self-decomposability and conditions for random variables of this type to be embedded into a stationary Ornstein-Uhlenbeck process

Wrong But Reasonable : The Fourth Amendment Particularity Requirement After United States v. Leon

This Note analyzes the application of the good-faith exception to search warrant particularity violations under the Fourth Amendment. The question compelled by United States v. Leon and Massachusetts v. Sheppard is when, if ever, a particularity-defective warrant will sustain an officer\u27s reasonable reliance.\u27\u27 The Note briefly discusses how particularity traditionally has been assessed under the fourth amendment. The author examines the Supreme Court\u27s holding in Massachusetts v. Sheppard, and contrasts several circuit court cases that have applied Sheppard\u27s objectively reasonable standard of good faith to warrants involving particularity defects. Finally, the Note concludes that the approach taken by the Second Circuit Court of Appeals in United States v. Buck is a preferable approach because it encourages courts to establish clearer standards for the particularity of warrants under the Fourth Amendment