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Showing 1 to 20 of 27 for “"Martingales"”.
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Martingales in Filtering and Geometry
We give three applications of martingale theory. First, we study a problem in real-time target tracking. Realistic assumptions, namely limited processing power, turn the variance into a stochastic process. We transform and compensate the variance process so as to obtain a martingale. We find …
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Martingales, Singular Integrals, and Fourier Multipliers
<p>Many probabilistic constructions have been created to study the <em>Lp</em>-boundedness, 1 < <em>p</em> < ∞, of singular integrals and Fourier multipliers. We will use a combination of analytic and probabilistic methods to study analytic properties of these constructions and obtain results which …
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Pointwise Relations Between Ergodic Averages and Martingales
It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining …
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Extremal functions related to convexity and martingales
We consider the problem of finding the extremal function in the class of real-valued biconvex functions satisfying a boundary condition on a product of the unit ball with itself, with a suitable norm in the plane. We want to maximize the biconvex function at a point in the domain where the second …
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Some sharp inequalities for conditionally symmetric martingales
Let f be a conditionally symmetric martingale taking values in a Hilbert space $\rm I\!H$ and let S(f) be its square function. If $\nu\sb{\rm p}$ is the smallest positive zero of the confluent hypergeometric function and $\mu\sb{\rm p}$ is the largest positive zero of the parabolic cylinder …
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A Weak Type Inequality for Martingale Transforms and Other Subordinate Martingales
… martingale case. We present examples of martingales that give good lower estimates of the best constant. We then find a biconcave function to prove that the supremum of these lower estimates is in fact the best constant. We use this biconcave function to prove a sharp weak type inequality …
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Inequalities for the differential subordinates of Martingales, harmonic functions and Ito processes
In Chapter 1 we sharpen Burkholder's inequality $\mu(\vert v\vert\geq1)\leq2\Vert u\Vert\sb1$ for two harmonic functions u and v by adjoining an extra assumption. That is, we prove the weak-type inequality $\mu(\vert v\vert\geq1)\leq K\Vert u\Vert\sb1$ under the assumptions that $\vert …
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The Theory of Martingales in an S-Finite Measure Space Indexed by Directed Sets
Made available in DSpace on 2014-12-05T21:50:10Z (GMT). No. of bitstreams: 1 5801689.pdf: 2376590 bytes, checksum: 8010e244d27993a27142c7a250b8eab0 (MD5) Previous issue date: 1958
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Nearly Representable Operators (dunford-Pettis, Radon-Nikodym)
… operators that map X-valued uniformly bounded martingales that are Cauchy in the Pettis norm into Y-valued martingales that converge almost everywhere.
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Some Sharp Inequalities for Martingale Transforms
… their extensions to differentially subordinate martingales.
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Adaptive Control and Parameter Estimation in Markov Chains: A Quadratic Case
… processes. In the second chapter, we introduce Martingales and discuss some of their important properties. Martingales are important tools used in the methods of parameter estimation of Markov chains in the later chapters. In the third chapter, we focus on adaptive control of Markov chains. …
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Cox-type model validation with recurrent event data
… are obtained using the counting processes and martingales machinery techniques. Asymptotic properties of the proposed estimators and how they can be used to construct confidence intervals are investigated. The results of the simulation studies assessing the performance of the estimators and an …
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Essays On The Mathematics Of Market Efficiency
… results on filtration shrinkage for strict local martingales.
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Stochastic Modelling and Optimal Control of Compartment Fires
… differential equations based on the theory of Martingales is presented. In part two of the thesis, two deterministic models based on the risk assessment model of the National Research Council Canada (NRCC) are developed and calibrated. One of the deterministic models is a fuel driven model and …
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A Problem From Hamiltonian Mechanics With Time -Periodic Coefficients, Small Noise, and Degeneracy
… and are related to the description of spider martingales. The dynamics of the reduced process can also be understood through the Fokker-Planck equation, and the gluing coefficients arise in the corresponding conservation of flux and in the continuity equation.
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On the occurrences of motifs in recursive trees, with applications to random structures
… urn theory, moment generating functions and martingales.</p>
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Computability and Fractal Dimension
… Hausdorff dimension. Using resource-bounded martingales, we are able to transfer the use of r-expansiveness to the resource-bounded case, which enables us to show that the Small-Span Theorem does not hold for dimension in exponential time E. Finally, we investigate the effective Hausdorff …
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L'approche moderne de l'étude mathématique des phénomènes de transition de phases
… introduire quelques résultats de convergence des martingales renversées, celles-ci étant utilisées à la fin du chapitre 3. Un troisième résultat auquel nous ferons appel lors de la description des phénomènes de transitions de phases selon l'approche moderne, est celui qui stipule que dans notre …
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Martingale Convergence Techniques in Noncommutative Integration
… techniques and constructions from the theory of martingales and Banach space geometry to solve problems in noncommutative analysis. The first problem we study is norm convergence for the Fourier transform of the noncommutative Vilenkin system. By using martingale constructions and techniques from …
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Polynomial Multi-Curve Models And Extensions In Mathematical Finance
… the discounted zero-coupon bond prices are local martingales. In the third chapter, we consider a specific type of volatility models, which all have the characteristic that the moments of the stock can be expressed as a polynomial. Further, we show that there is a relation between the k-th moment …
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