Stochastic differential equations (SDEs) are used to describe dynamical systems subject to random variations. They are widely applied in many fields when the noise affects the system. The IMATI group "stochastic differential equations" is mainly interested in the applications of SDEs in biology, finance and engineering.  


SDEs are suitable to representing biological systems, in particular population dynamics where the state variables describe, for example, population densities. In this framework, an acarine predator-prey stochastic differential systems has been considered and methods of parameters estimation in SDEs, based on MCMC, have been developed. Following the same rationale, SDEs are applied to describe the dynamics of uninfected and infected cells during a Chlamydial infection.

 

In finance, SDEs are widely used to describe the dynamics of a security price. The group has developed methods for the evaluation of non-standard options where the dynamics of the underlying asset and of its stochastic volatility are represented through SDEs.

In the industrial field, the description of many processes is linked to differential systems, the coefficients of which are often unknown or known with uncertainty. In this context, the group has developed and experimentally validated  estimation methods of the thermal conductivity in polymers, with a simpler layout than that prescribed by the current regulations and with the ability to assess  the uncertainty associated with the estimates.

 

 

People:

Eettore Lanzarone Sara Pasquali Fabrizio Ruggeri

 

References:

F. D’Ippoliti, E. Moretto, S. Pasquali, B. Trivellato Exact pricing with stochastic volatility and jumps, Int. J.  Theoretical Appl. Finance, 13(6) (2010),  901-929.

G. Gilioli, S. Pasquali, F. Ruggeri Nonlinear functional response parameter estimation in a stochastic predator-prey model Math. Biosci.  Eng. 9(12) (2012), 75-96.

E. Lanzarone, S. Pasquali, V. Mussi, F. Ruggeri Bayesian estimation of thermal conductivity and temperature profile in a homogeneous mass, Numer Heat Tr. B, 66 (2014), 397-421.

 

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