References of "Azmoodeh, Ehsan 50000534"
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See detailThe law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds
Azmoodeh, Ehsan UL; Peccati, Giovanni UL; Poly, Guillaume

in ALEA: Latin American Journal of Probability and Mathematical Statistics (2016), 13

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See detailGeneralization of the Nualart-Peccati criterion
Azmoodeh, Ehsan UL; Malicet, Dominique; Mijoule, Guillaume et al

in Annals of Probability (2015), 44

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See detailAsymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri

in Modern Stochastics: Theory and Applications (2015), 2(1), 2949

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See detailOptimal Berry-Esseen bounds on the Poisson space.
Peccati, Giovanni UL; Azmoodeh, Ehsan UL

E-print/Working paper (2015)

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See detailParameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind
Azmoodeh, Ehsan UL; Viitasaari, Lauri

in Statistical Inference for Stochastic Processes (2015), 18(3), 205227

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See detailConvergence towards linear combinations of chi-squared random variables: a Malliavin-based approach.
Azmoodeh, Ehsan UL; Peccati, Giovanni UL; Poly, Guillaume

in Séminaire de Probabilités XLVII (2015)

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See detailNecessary and sufficient conditions for Hölder continuity of Gaussian processes
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri et al

in Statistics & Probability Letters (2014), 94

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note ... [more ▼]

The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. [less ▲]

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See detailFourth Moment Theorems for Markov diffusion generators
Azmoodeh, Ehsan UL; Campese, Simon UL; Poly, Guillaume Joseph UL

in Journal of Functional Analysis (2014), 266(4), 23412359

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion ... [more ▼]

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We are not only able to drastically simplify all of its previous proofs, but also to provide new settings of diffusive generators (Laguerre, Jacobi) where such a criterion holds. Convergence towards Gamma and Beta distributions under moment conditions is also discussed. [less ▲]

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See detailA general approach to small deviation via concentration of measures
Azmoodeh, Ehsan UL; Viitasaari, Lauri

E-print/Working paper (2014)

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See detailAsymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model
Azmoodeh, Ehsan UL; Sottinen, Tommi; Viitasaari, Lauri

E-print/Working paper (2014)

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst ... [more ▼]

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional part satisfies H∈(3/4,1), the central limit theorem holds. In the nonsemimartingale case, that is, where H∈(1/2,3/4], the convergence toward the normal distribution with a nonzero mean still holds if H=3/4, whereas for the other values, that is, H∈(1/2,3/4), the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator. [less ▲]

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See detailSpectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion
Azmoodeh, Ehsan UL; Valkeila, Esko

in Statistical Inference for Stochastic Processes (2013), 16(2), 97-112

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same ... [more ▼]

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy. [less ▲]

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See detailParameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind
Azmoodeh, Ehsan UL; Viitasaari, Lauri

E-print/Working paper (2013)

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See detailRate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion
Azmoodeh, Ehsan UL; Viitasaari, Lauri

in Journal of Theoretical Probability (2013)

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a ... [more ▼]

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a large class of convex functions $f$ is considered. In $\big[$\cite{a-m-v}, Statistics \& Decisions, \textbf{27}, 129-143$\big]$, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrary close to $H - \frac{1}{2}$. [less ▲]

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See detailDrift parameter estimation for fractional Ornstein–Uhlenbeck process of the second kind
Azmoodeh, Ehsan UL; Morlanes, Jose Igor

in Statistics: A Journal of Theoretical and Applied Statistics (2013)

The fractional Ornstein–Uhlenbeck process of the second kind (fOU2) is the solution of the Langevin equation with driving noise where B is a fractional Brownian motion with Hurst parameter H(0, 1). In ... [more ▼]

The fractional Ornstein–Uhlenbeck process of the second kind (fOU2) is the solution of the Langevin equation with driving noise where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>½, we prove that the least-squares estimator introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein–Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11–12):1030–1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(½, 1). [less ▲]

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See detailOn the fractional Black-Scholes market with transaction costs
Azmoodeh, Ehsan UL

in Communications in Mathematical Finance (2013), 2(3), 21-40

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1 ... [more ▼]

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the case when the transaction costs coefficients decrease as $n^{-(1-H)}$. We study the expected hedging error and asymptotic behavior of the hedge as Hurst parameter $H$ approaches $\frac{1}{2}$. [less ▲]

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