# Symbolic Calculus in Mathematical Statistics: A Review

@article{Nardo2015SymbolicCI, title={Symbolic Calculus in Mathematical Statistics: A Review}, author={E. Nardo}, journal={arXiv: Statistics Theory}, year={2015}, pages={1-72} }

In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical umbral calculus, as introduced by Rota and Taylor in $1994.$ The usefulness of this symbolic technique is twofold. The first is to show how new algebraic identities drive in discovering insights among topics apparently very far from each other and related to… Expand

#### 5 Citations

On multivariable cumulant polynomial sequences with applications

- Mathematics
- 2016

A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these… Expand

Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix

- Computer Science, Mathematics
- J. Multivar. Anal.
- 2020

This paper shows how the umbral operator accomplishes the employment of a suitable linear operator in place of hypergeometric functions and zonal polynomials and represents an alternative tool to deal with these symmetric functions. Expand

A cumulant approach for the first-passage-time problem of the Feller square-root process

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2021

The resulting procedure is made easier to implement by the symbolic calculus and a rational choice of the polynomial degree depending on skewness, kurtosis and hyperskewness and some case studies show the goodness of the approximation even for a low number of terms. Expand

On the Cumulants of the First Passage Time of the Inhomogeneous Geometric Brownian Motion

- Mathematics
- 2021

We consider the problem of the first passage time T of an inhomogeneous geometric Brownian motion through a constant threshold, for which only limited results are available in the literature. In the… Expand

On non-linear dependence of multivariate subordinated Lévy processes

- Mathematics
- 2020

Multivariate subordinated Levy processes are widely employed in finance for modeling multivariate asset returns. We propose to exploit non-linear dependence among financial assets through… Expand

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