Search results for "Weak convergence"

showing 4 items of 14 documents

The coalescent in population models with time-inhomogeneous environment

2002

AbstractThe coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.

Statistics and ProbabilityWeak convergencePopulation geneticsApplied MathematicsPopulation sizeVarying environmentPopulation geneticsProduct integralHeavy traffic approximationProduct integralStirling numbersCoalescent theoryFamily SizesDiffusion approximationPopulation modelAncestorsModelling and SimulationModeling and SimulationEconometricsQuantitative Biology::Populations and EvolutionCoalescentStatistical physicsWeak convergenceMathematicsStochastic Processes and their Applications
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Convergence rate of a relaxed inertial proximal algorithm for convex minimization

2018

International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Class (set theory)Control and OptimizationInertial frame of referenceLyapunov analysis0211 other engineering and technologies02 engineering and technologyManagement Science and Operations Research01 natural sciencessymbols.namesakenonsmooth convex minimizationrelaxationweak-convergence0101 mathematics[MATH]Mathematics [math]point algorithmMathematics021103 operations researchWeak convergence[QFIN]Quantitative Finance [q-fin]Applied MathematicsHilbert space[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]dynamicsmaximally monotone operatorsInertial proximal method010101 applied mathematicsMonotone polygonRate of convergenceConvex optimizationmaximal monotone-operatorssymbolsRelaxation (approximation)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]subdifferential of convex functionsAlgorithm
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Convergence rate of the Euler scheme for diffusion processes

2006

strong convergenceEuler schemeweak convergencestochastic differential equations
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Convergence of Measures

2020

One focus of probability theory is distributions that are the result of an interplay of a large number of random impacts. Often a useful approximation can be obtained by taking a limit of such distributions, for example, a limit where the number of impacts goes to infinity. With the Poisson distribution, we have encountered such a limit distribution that occurs as the number of very rare events when the number of possibilities goes to infinity (see Theorem 3.7). In many cases, it is necessary to rescale the original distributions in order to capture the behavior of the essential fluctuations, e.g., in the central limit theorem. While these theorems work with real random variables, we will a…

symbols.namesakeProbability theoryWeak convergencesymbolsLimit (mathematics)Statistical physicsPoisson distributionConvergence of measuresRandom variableBrownian motionMathematicsCentral limit theorem
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