Related papers: Cumulant Expansion and Monthly Sum Derivative
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zheng on the single variable case. As an application, for…
We establish an explicit connection between a Davenport expansion and the Popov sum. Asymptotic analysis follows as a result of these formulas. New solutions to a query of N.J. Fine are offered, and a proof of Davenport expansions is…
The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved…
This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones…
In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \cite{Yoshida2013}, which establishes Edgeworth…
Writing for a general mathematical audience, we provide elementary upper and lower bounds on the growth (as a function of N) of the sum \sum_{n=1}^N (-1)^{\floor{n x}} for various fixed x. For example, if x is a quadratic irrational, then…
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our…
We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…
Virial expansions are the series in powers of density assumed to be small. However, the equations of state require to consider finite densities for which virial expansions, as a rule, diverge. In order to extrapolate a virial expansion to…
The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on…
We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
We generalize the notion of essential closures which is used in formulating a geometric necessary condition for a set to be the support of a multivariate copula. Furthermore, in some special cases, we derive an explicit formula of the…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We establish an explicit approximation formula for European put option prices within a general stochastic volatility model with time-dependent parameters. Our methodology is based on expansions of the mixing representation of the put option…
This paper builds upon our recent work which computed the moment generating function of the MIMO mutual information exactly in terms of a Painlev\'{e} V differential equation. By exploiting this key analytical tool, we provide an in-depth…
We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included.