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A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

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Operator-Like Wavelet Bases of L-2(R-d)

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The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

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Ieee-Inst Electrical Electronics Engineers Inc2013

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

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In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...

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This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...

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Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

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We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

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Propagation Models for Biochemical Reaction Networks

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In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...

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Stochastic integrals for spde's: A comparison

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We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and ...

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Bedload transport on steep slope: a stochastic framework.

Christophe Ancey, Joris Heyman, François Mettra

Among the recent experimental studies focusing on the stochastic nature of bedload transport, some results are particularly intriguing: in experiments in which tagged particles (tracers) are tracked, the statistical moments of the time evolution of particl ...

2011