Search results for "60J65"

showing 3 items of 3 documents

Set-valued Brownian motion

2015

Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the paper of the second author in which an embedding result is obtained which considers also the ordered structure of $ck(X)$ and f-algebras.

Pure mathematicsGeneral MathematicsBanach spaceStructure (category theory)Vector LatticesSpace (mathematics)01 natural sciencesSet (abstract data type)Radstrom embedding theoremMathematics::ProbabilityFOS: MathematicsMarginal distributions0101 mathematicsBrownian motionMathematicsgeneralized Hukuhara differenceApplied MathematicsProbability (math.PR)010102 general mathematicsRegular polygonBrownian motion · Rådström embedding theorem · Vector lattices · Marginal distributions · Generalized Hukuhara difference60J65 58C06 46A40Functional Analysis (math.FA)010101 applied mathematicsMathematics - Functional AnalysisBrownian motion Radstrom embedding theorem Vector Lattices Marginal distributions generalized Hukuhara differenceEmbeddingBrownian motionMarginal distributionMathematics - Probability
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Large systems of path-repellent Brownian motions in a trap at positive temperature

2006

We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation princip…

Statistics and ProbabilityFOS: Physical scienceslarge deviationssymbols.namesakeQuantum systemFOS: MathematicsGross-Pitaevskii formula60J6560F10; 60J65; 82B10; 82B26Brownian motionMathematical PhysicsEnergy functionalMathematicsInteracting Brownian motionsStochastic process82B10Mathematical analysisProbability (math.PR)Brownian excursionMathematical Physics (math-ph)Brownian intersection local timessymbolsoccupation measure82B26Large deviations theoryStatistics Probability and UncertaintyHamiltonian (quantum mechanics)Rate functionMathematics - Probability60F10
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Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

2012

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

Statistics and ProbabilityPure mathematicsProbability (math.PR)coexistenceType (model theory)Characterization (mathematics)Branching (polymer chemistry)Trotter productstochastic differential equationsLévy noisesegregation of typesStochastic differential equationKernel (algebra)Mutually catalytic branching60G1760K35Convergence (routing)FOS: Mathematics60J6560J55PreprintStatistics Probability and UncertaintyMathematics - ProbabilityMathematicsBranching processThe Annals of Probability
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