Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations

Kouji Yano

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Displaying similar documents to “Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations”

Density of paths of iterated Lévy transforms of brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.

Density of paths of iterated Lévy transforms of Brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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α-time fractional brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when is a stable subordinator, can arise as scaling limit...

α-time fractional Brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy

Jean Brossard, Christophe Leuridan (2012)

Annales de l'I.H.P. Probabilités et statistiques

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Let be a measurable transformation of a probability space $(E, ℰ, π)$ , preserving the measure. Let be a random variable with law . Call (⋅, ⋅) a regular version of the conditional law of given (). Fix $B \in ℰ$ . We first prove that if is reachable from -almost every point for a Markov chain of kernel , then the -orbit of -almost every point visits . We then apply this result to the Lévy transform, which transforms the Brownian motion into the Brownian motion || − , where is the local time at 0...

Semimartingale decomposition of convex functions of continuous semimartingales by brownian perturbation

Nastasiya F. Grinberg (2013)

ESAIM: Probability and Statistics

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In this note we prove that the local martingale part of a convex function of a -dimensional semimartingale = + can be written in terms of an Itô stochastic integral ∫()d, where () is some particular measurable choice of subgradient ∇ f ( x ) of at , and is the martingale part of . This result was first proved by Bouleau in [N. Bouleau, 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for $\tilde{X} = X + ϵ B$ x10ff65; X = X + ϵB , > 0, where is...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2011)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some ∈ (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when neglecting...

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

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Let be a complete Riemannian manifold, ∈ ℕ and ≥ 1. We prove that almost everywhere on = ( ,, ) ∈ for Lebesgue measure in , the measure $μ (x) = N \sum_{k = 1}^{N} x_{k}$ μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...

Survival probabilities of autoregressive processes

Christoph Baumgarten (2014)

ESAIM: Probability and Statistics

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Given an autoregressive process of order ( = + ··· + + where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

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Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....

Hydrodynamic limit of a d-dimensional exclusion process with conductances

Fábio Júlio Valentim (2012)

Annales de l'I.H.P. Probabilités et statistiques

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Fix a polynomial of the form () = + ∑2≤≤ =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on $𝕋^{d}$ , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑ ...

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

Luís Balsa Bicho, António Ornelas (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem inf{ () + () + (1 − − ) () | Ω open in ℝ, || ≤ 1}, for ∈ [0, 1], + ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.