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We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow...

Lois de martingale, densités et décomposition de Föllmer Schweizer

Jean-Pascal Ansel, Christophe Stricker (1992)

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

Long-memory stable Ornstein-Uhlenbeck processes.

Maejima, Makoto, Yamamoto, Kenji (2003)

Electronic Journal of Probability [electronic only]

Long-term behavior for superprocesses over a stochastic flow.

Xiong, Jie (2004)

Electronic Communications in Probability [electronic only]

Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients

Igor D. Chueshov, Pierre-A. Vuillermot (1998)

Annales de l'I.H.P. Analyse non linéaire

Low-variance direct Monte Carlo simulations using importance weights

Husain A. Al-Mohssen, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present an efficient approach for reducing the statistical uncertainty associated with direct Monte Carlo simulations of the Boltzmann equation. As with previous variance-reduction approaches, the resulting relative statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the characteristic value of quantity of interest) is small and independent of the magnitude of the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible....

Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

Raluca M. Balan (2011)

ESAIM: Probability and Statistics

In this article, we consider the stochastic heat equation $d u = (Δ u + f (t, x)) d t + \sum_{k = 1}^{\infty} g^{k} (t, x) δ β_{t}^{k}, t \in [0, T]$ , with random coefficientsf and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.

Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise*

Raluca M. Balan (2012)

ESAIM: Probability and Statistics

In this article, we consider the stochastic heat equation $d u = (Δ u + f (t, x)) d t + \sum_{k = 1}^{\infty} g^{k} (t, x) δ β_{t}^{k}, t \in [0, T]$ , with random coefficients f and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.

Lyapunov exponents for stochastic differential equations on semi-simple Lie groups

Paulo R. C. Ruffino, Luiz A. B. San Martin (2001)

Archivum Mathematicum

With an intrinsic approach on semi-simple Lie groups we find a Furstenberg–Khasminskii type formula for the limit of the diagonal component in the Iwasawa decomposition. It is an integral formula with respect to the invariant measure in the maximal flag manifold of the group (i.e. the Furstenberg boundary $B = G / M A N$ ). Its integrand involves the Borel type Riemannian metric in the flag manifolds. When applied to linear stochastic systems which generate a semi-simple group the formula provides a diagonal matrix...