Sectorial local non-determinism and the geometry of the Brownian sheet.
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Xiao, Yimin, Khoshnevisan, Davar, Wu, Dongsheng (2006)
Electronic Journal of Probability [electronic only]
Michna, Zbigniew (1998)
Journal of Applied Mathematics and Stochastic Analysis
Hiroshi Sato, Yoshiaki Okazaki (1975)
Annales de l'I.H.P. Probabilités et statistiques
Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2008)
ESAIM: Probability and Statistics
In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal...
S. Chevet (1977/1978)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
Linde, Werner, Ayache, Antoine (2009)
Electronic Journal of Probability [electronic only]
Giancarlo Mauceri, Stefano Meda, Peter Sjögren (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure on We prove a sharp estimate of the operator norm of the imaginary powers of on
Bernard Bercu, Fabrice Gamboa, Marc Lavielle (2000)
ESAIM: Probability and Statistics
Bernard Bercu, Fabrice Gamboa, Marc Lavielle (2010)
ESAIM: Probability and Statistics
Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical...
Nikitin, Ya.Yu., Orsingher, E. (2004)
Zapiski Nauchnykh Seminarov POMI
Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier (2006)
Annales de l'I.H.P. Probabilités et statistiques
Frank Aurzada, Thomas Simon (2007)
ESAIM: Probability and Statistics
We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function with a real SαS Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of f at zero, which extends the results of Lifshits and Simon, Ann. Inst. H. Poincaré Probab. Statist.41 (2005) 725–752 where this was proved for f being a power function (Riemann-Liouville processes). In the Gaussian case, the same generality as...
Rafał Latała, Krzysztof Oleszkiewicz (2005)
Studia Mathematica
A certain inequality conjectured by Vershynin is studied. It is proved that for any symmetric convex body K ⊆ ℝⁿ with inradius w and γₙ(K) ≤ 1/2 we have for any s ∈ [0,1], where γₙ is the standard Gaussian probability measure. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.
Mikhail Lifshits, Thomas Simon (2005)
Annales de l'I.H.P. Probabilités et statistiques
Lifshits, Mikhail, Linde, Werner, Shi, Zhan (2006)
Electronic Journal of Probability [electronic only]
Michel Talagrand (1988)
Annales de l'I.H.P. Probabilités et statistiques
Mario Wschebor (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the smoothed paths. Various classes of stochastic processes are considered starting with the Wiener process,...
Guangjun Shen, Litan Yan, Chao Chen (2012)
Czechoslovak Mathematical Journal
Let , be two independent, -dimensional bifractional Brownian motions with respective indices and . Assume . One of the main motivations of this paper is to investigate smoothness of the collision local time where denotes the Dirac delta function. By an elementary method we show that is smooth in the sense of Meyer-Watanabe if and only if .
Lanjri Zadi, Noureddine, Nualart, David (2003)
Electronic Communications in Probability [electronic only]
Philippe Berthet, Mikhail Lifshits (2002)
Annales de l'I.H.P. Probabilités et statistiques
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