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ISSN: 2333-9721

APC: Only $99 Submit 2020 ( 12 ) 2019 ( 93 ) 2018 ( 97 ) 2017 ( 112 ) Search Results: 1 - 10 of 53054 matches for " David Nualart " All listed articles are free for downloading (OA Articles)  Page 1 /53054 Display every page 5 10 20 Item  Arbor : Ciencia, Pensamiento y Cultura , 2004, Abstract: No disponible  Mathematics , 2004, Abstract: Let$B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$be a$d$-dimensional fractional Brownian motion with Hurst parameter$H$and let$R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$be the fractional Bessel process. It\^{o}'s formula for the fractional Brownian motion leads to the equation$ R_{t}=\sum_{i=1}^{d}\int_{0}^{t}\frac{B_{s}^{i}}{R_{s}}% dB_{s}^{i}+H(d-1)\int_{0}^{t}\frac{s^{2H-1}}{R_{s}}ds . $In the Brownian motion case ($H=1/2$),$X_{t}=\sum_{i=1}^{d}\int_{0}^{t} frac{B_{s}^{i}}{% R_{s}}dB_{s}^{i}$is a Brownian motion. In this paper it is shown that$X_{t}$is \underbar{not} a fractional Brownian motion if$H\not=1/2$. We will study some other properties of this stochastic process as well.  Mathematics , 2006, Abstract: Using fractional calculus we define integrals of the form$% \int_{a}^{b}f(x_{t})dy_{t}$, where$x$and$y$are vector-valued H\"{o}lder continuous functions of order$\displaystyle \beta \in (\frac13, \frac12)$and$f$is a continuously differentiable function such that$f'$is$\lambda$-H\"oldr continuous for some$\lambda>\frac1\beta-2$. Under some further smooth conditions on$f$the integral is a continuous functional of$x$,$y$, and the tensor product$x\otimes y$with respect to the H\"{o}lder norms. We derive some estimates for these integrals and we solve differential equations driven by the function$y$. We discuss some applications to stochastic integrals and stochastic differential equations.  Mathematics , 2006, DOI: 10.1214/009117905000000288 Abstract: We study the two-dimensional fractional Brownian motion with Hurst parameter$H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.  Mathematics , 2007, Abstract: In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally Gaussian random variable. Some applications to sequences of multiple stochastic integrals, and renormalized weighted Hermite variations of the fractional Brownian motion are discussed.  Mathematics , 2007, Abstract: We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of solutions of a linear heat equation with multiplicative white noise. Then we settle this question by proving that solutions to the linear equation have negative moments of all orders.  Mathematics , 2009, Abstract: We study a least squares estimator$\hat {\theta}_T$for the Ornstein-Uhlenbeck process,$dX_t=\theta X_t dt+\sigma dB^H_t$, driven by fractional Brownian motion$B^H$with Hurst parameter$H\ge \frac12$. We prove the strong consistence of$\hat {\theta}_T$(the almost surely convergence of$\hat {\theta}_T$to the true parameter${% \theta}$). We also obtain the rate of this convergence when$1/2\le H<3/4$, applying a central limit theorem for multiple Wiener integrals. This least squares estimator can be used to study other more simulation friendly estimators such as the estimator$\tilde \theta_T$defined by (4.1).  Mathematics , 2009, Abstract: The purpose of this note is to prove a central limit theorem for the$L^3$-modulus of continuity of the Brownian local time using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's theorem and the Clark-Ocone formula for the$L^3$-modulus of the Brownian local time.  Mathematics , 2012, DOI: 10.1080/17442508.2013.774403 Abstract: We construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart.  Mathematics , 2012, Abstract: We prove a central limit theorem for functionals of two independent$d$-dimensional fractional Brownian motions with the same Hurst index$H$in$(\frac{2}{d+1},\frac{2}{d})\$ using the method of moments.
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