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Malliavin-Stein method: a survey of some recent developments Azmoodeh, Ehsan ; Peccati, Giovanni ; Yang, Xiaochuan in Modern Stochastics: Theory and Applications (2021), 8(2), 141-177 Detailed reference viewed: 49 (0 UL)The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds Azmoodeh, Ehsan ; Peccati, Giovanni ; in ALEA: Latin American Journal of Probability and Mathematical Statistics (2016), 13 Detailed reference viewed: 121 (2 UL)Generalization of the Nualart-Peccati criterion Azmoodeh, Ehsan ; ; et al in Annals of Probability (2015), 44 Detailed reference viewed: 127 (9 UL)Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind Azmoodeh, Ehsan ; in Statistical Inference for Stochastic Processes (2015), 18(3), 205227 Detailed reference viewed: 112 (1 UL)Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach. Azmoodeh, Ehsan ; Peccati, Giovanni ; in Séminaire de Probabilités (2015) Detailed reference viewed: 218 (17 UL)Optimal Berry-Esseen bounds on the Poisson space. Peccati, Giovanni ; Azmoodeh, Ehsan E-print/Working paper (2015) Detailed reference viewed: 71 (0 UL)Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model Azmoodeh, Ehsan ; ; in Modern Stochastics: Theory and Applications (2015), 2(1), 2949 Detailed reference viewed: 96 (6 UL)Necessary and sufficient conditions for Hölder continuity of Gaussian processes Azmoodeh, Ehsan ; ; et al in Statistics and 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 ▲] Detailed reference viewed: 101 (1 UL)Fourth Moment Theorems for Markov diffusion generators Azmoodeh, Ehsan ; Campese, Simon ; Poly, Guillaume Joseph 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 ▲] Detailed reference viewed: 189 (27 UL)Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model Azmoodeh, Ehsan ; ; 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 ▲] Detailed reference viewed: 103 (0 UL)A general approach to small deviation via concentration of measures Azmoodeh, Ehsan ; E-print/Working paper (2014) Detailed reference viewed: 52 (0 UL)Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion Azmoodeh, Ehsan ; 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 ▲] Detailed reference viewed: 108 (0 UL)Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind Azmoodeh, Ehsan ; E-print/Working paper (2013) Detailed reference viewed: 91 (1 UL)Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion Azmoodeh, Ehsan ; 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 ▲] Detailed reference viewed: 144 (4 UL)Drift parameter estimation for fractional Ornstein–Uhlenbeck process of the second kind Azmoodeh, Ehsan ; 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 ▲] Detailed reference viewed: 160 (6 UL)On the fractional Black-Scholes market with transaction costs Azmoodeh, Ehsan 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 ▲] Detailed reference viewed: 109 (2 UL) |
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