Riccardo Passeggeri
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Previous Organizations / Institutes
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Research Subjects
Riccardo Passeggeri has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Almut E. D. Veraart
Department of Mathematics Imperial College London 180 Queen's Gate SW7 2AZ London UK
3 shared publications Olivier Wintenberger
LPSM
1 shared publication
Latest Publications
- Open Access
Extremes for stationary regularly varying random fields over arbitrary index sets
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature [3, 21]. However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure [23] except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space [18], the $\upsilon$-spectral tail measure provides a natural extension that describes the clustering effect in full generality.
Open AccessExtremes for stationary regularly varying random fields over arbitrary index sets
We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature [3, 21]. However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure [23] except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space [18], the $\upsilon$-spectral tail measure provides a natural extension that describes the clustering effect in full generality.
- 1 March 2020
- Published by Elsevier in Stochastic Processes and their Applications
- Vol. 130 (3) , 1226-1257
On the signature and cubature of the fractional Brownian motion for- 1 March 2020
- Published by Elsevier in Stochastic Processes and their Applications
- Vol. 130 (3) , 1226-1257
On the signature and cubature of the fractional Brownian motion for- Open Access
Spectral representations of quasi-infinitely divisible processes
In this work we first introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Then, we introduce QID stochastic integrals and present integrability conditions and continuity properties. Further, we introduce QID stochastic processes, i.e. stochastic processes with QID finite dimensional distributions. For example, a process $X$ is QID if there exist two ID processes $Y$ and $Z$ such that $X+Y\stackrel{d}{=}Z$ with $Y$ independent of $X$. The class of QID processes is strictly larger than the class of ID processes. We provide spectral representations and L\'{e}vy-Khintchine formulations for potentially all QID processes. Finally, we prove that QID random measures are dense in the space of random measures under convergence in distribution. Throughout this work we present many examples.Open AccessSpectral representations of quasi-infinitely divisible processes
In this work we first introduce quasi-infinitely divisible (QID) random measures and formulate spectral representations. Then, we introduce QID stochastic integrals and present integrability conditions and continuity properties. Further, we introduce QID stochastic processes, i.e. stochastic processes with QID finite dimensional distributions. For example, a process $X$ is QID if there exist two ID processes $Y$ and $Z$ such that $X+Y\stackrel{d}{=}Z$ with $Y$ independent of $X$. The class of QID processes is strictly larger than the class of ID processes. We provide spectral representations and L\'{e}vy-Khintchine formulations for potentially all QID processes. Finally, we prove that QID random measures are dense in the space of random measures under convergence in distribution. Throughout this work we present many examples. - Open Access
- 1 October 2018
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 32 (4) , 1845-1879
Mixing Properties of Multivariate Infinitely Divisible Random Fields
- 1 October 2018
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 32 (4) , 1845-1879
Open AccessMixing Properties of Multivariate Infinitely Divisible Random Fields
- Open Access
Limit theorems for multivariate Brownian semistationary processes and feasible results
In this paper we introduce the \textit{multivariate} Brownian semistationary (BSS) processes and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general stationary multivariate Gaussian processes, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.
Open AccessLimit theorems for multivariate Brownian semistationary processes and feasible results
In this paper we introduce the \textit{multivariate} Brownian semistationary (BSS) processes and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general stationary multivariate Gaussian processes, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.
- Open AccessSome results on the Signature and Cubature of the Fractional Brownian motion for $H>\frac{1}{2}$In this work we present different results concerning the signature and the cubature of fractional Brownian motion (fBm). The first result regards the rate of convergence of the expected signature of the linear piecewise approximation of the fBm to its exact value, for a value of the Hurst parameter $H\in(\frac{1}{2},1)$. We show that the rate of convergence is given by $2H$. We believe that this rate is sharp as it is consistent with the result of Ni and Xu, who showed that the sharp rate of convergence for the Brownian motion (i.e. fBm with $H=\frac{1}{2}$) is given by $1$. The second result regards the bound of the coefficient of the rate of convergence obtained in the first result. We obtain an uniform bound for the coefficient for the $2k$-th term of the signature of $\frac{\tilde{A}k(2k-1)}{(k-1)!2^{k}}$, where $\tilde{A}$ is a finite constant independent of $k$. The third result regards the sharp decay rate of the expected signature of the fBm. We obtain a sharp bound for the $2k$-th term of the expected signature of $\frac{1}{k!2^{k}}$. The last results concern the cubature method for the fBm for $H>\frac{1}{2}$. In particular, we develop the framework of the cubature method for fBm, provide a bound for the approximation error in the general case, and obtain the cubature formula for the fBm in a particular setting. These results extend the work of Lyons and Victoir, who focused on the Brownian motion case.Open AccessSome results on the Signature and Cubature of the Fractional Brownian motion for $H>\frac{1}{2}$In this work we present different results concerning the signature and the cubature of fractional Brownian motion (fBm). The first result regards the rate of convergence of the expected signature of the linear piecewise approximation of the fBm to its exact value, for a value of the Hurst parameter $H\in(\frac{1}{2},1)$. We show that the rate of convergence is given by $2H$. We believe that this rate is sharp as it is consistent with the result of Ni and Xu, who showed that the sharp rate of convergence for the Brownian motion (i.e. fBm with $H=\frac{1}{2}$) is given by $1$. The second result regards the bound of the coefficient of the rate of convergence obtained in the first result. We obtain an uniform bound for the coefficient for the $2k$-th term of the signature of $\frac{\tilde{A}k(2k-1)}{(k-1)!2^{k}}$, where $\tilde{A}$ is a finite constant independent of $k$. The third result regards the sharp decay rate of the expected signature of the fBm. We obtain a sharp bound for the $2k$-th term of the expected signature of $\frac{1}{k!2^{k}}$. The last results concern the cubature method for the fBm for $H>\frac{1}{2}$. In particular, we develop the framework of the cubature method for fBm, provide a bound for the approximation error in the general case, and obtain the cubature formula for the fBm in a particular setting. These results extend the work of Lyons and Victoir, who focused on the Brownian motion case.
- Open Access
Mixing properties of multivariate infinitely divisible random fields
In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions for mixing of stationary ID multivariate random fields in terms of their spectral representation. Second, we prove that (linear combinations of independent) mixed moving average fields are mixing. Further, using a simple modification of the proofs of our results we are able to obtain weak mixing versions of our results. Finally, we prove the equivalence of ergodicity and weak mixing for multivariate ID stationary random fields.
Open AccessMixing properties of multivariate infinitely divisible random fields
In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions for mixing of stationary ID multivariate random fields in terms of their spectral representation. Second, we prove that (linear combinations of independent) mixed moving average fields are mixing. Further, using a simple modification of the proofs of our results we are able to obtain weak mixing versions of our results. Finally, we prove the equivalence of ergodicity and weak mixing for multivariate ID stationary random fields.