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Convergence rates for the full gaussian rough paths

Peter Friz, Sebastian Riedel (2014)

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

Under the key assumption of finite $ρ$ -variation, $ρ \in [1, 2)$ , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), $ρ = 1$ resp. $ρ = 1 / (2 H)$ , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate $k^{- (1 / ρ - 1 / 2 - ε)}$ , any $ε g t; 0$ , for Wong–Zakai and Milstein-type...

Convergence rates for weighted sums of random variables with random indices

D. Szynal, A. Zapała (1977)

Colloquium Mathematicae

Convergence to zero and boundedness of operator-normed sums of random vectors with application to autoregression processes.

Buldygin, V.V., Koval, V.A. (2001)

Georgian Mathematical Journal

Convergences de Martingales a valeurs Vectorielles

Metivier M. (1964)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Convex analysis for sets of local martingales measures

Josef Štěpán, P. Ševčík (2000)

Acta Universitatis Carolinae. Mathematica et Physica

Convex concentration inequalities and forward-backward stochastic calculus.

Klein, Thierry, Ma, Yutao, Privault, Nicolas (2006)

Electronic Journal of Probability [electronic only]

Convex hulls, Sticky particle dynamics and Pressure-less gas system

Octave Moutsinga (2008)

Annales mathématiques Blaise Pascal

We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities $u_{0}$ with negative jumps. We show the existence of a stochastic process and a forward flow $φ$ satisfying $X_{s + t} = φ (X_{s}, t, P_{s}, u_{s})$ and $d X_{t} = E [u_{0} (X_{0}) / X_{t}] d t$ , where $P_{s} = P X_{s}^{- 1}$ is the law of $X_{s}$ and $u_{s} (x) = E [u_{0} (X_{0}) / X_{s} = x]$ is the velocity of particle $x$ at time $s \geq 0$ . Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map $(x, t) \mapsto M (x, t) : = P (X_{t} \leq x)$ is the entropy solution of a scalar conservation law $\partial_{t} M + \partial_{x} (A (M)) = 0$ where the flux $A$ represents the particles...

Convex orderings for stochastic processes

Bruno Bassan, Marco Scarsini (1991)

Commentationes Mathematicae Universitatis Carolinae

We consider partial orderings for stochastic processes induced by expectations of convex or increasing convex (concave or increasing concave) functionals. We prove that these orderings are implied by the analogous finite dimensional orderings.

Convex rearrangements of Lévy processes

Youri Davydov, Emmanuel Thilly (2007)

ESAIM: Probability and Statistics

In this paper we study asymptotic behavior of convex rearrangements of Lévy processes. In particular we obtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measure is regularly varying at + with exponent α ∈ (1,2).