A5073817512- Stochastic processes and financial applications
- Stochastic processes and statistical mechanics
- Theoretical and Computational Physics
- Financial Risk and Volatility Modeling
- Complex Systems and Time Series Analysis
- Mathematical Analysis and Transform Methods
- Random Matrices and Applications
- Spectral Theory in Mathematical Physics
- Mathematical Dynamics and Fractals
- Quantum chaos and dynamical systems
- Mathematical and Theoretical Analysis
- Markov Chains and Monte Carlo Methods
- Rheology and Fluid Dynamics Studies
- Advanced Mathematical Modeling in Engineering
- Advanced Combinatorial Mathematics
- Cold Atom Physics and Bose-Einstein Condensates
- Stability and Controllability of Differential Equations
- Fractional Differential Equations Solutions
- advanced mathematical theories
- Growth Hormone and Insulin-like Growth Factors
- Material Dynamics and Properties
- Point processes and geometric inequalities
- Multiculturalism, Politics, Migration, Gender
- Health, Medicine and Society
- Stock Market Forecasting Methods
Centro Hospitalar do Porto
2024
Universidade Aberta
2010-2021
University of Lisbon
2011-2021
Centro Hospitalar de Vila Nova de Gaia
2018-2019
Fundação para a Ciência e Tecnologia
2006-2014
Bielefeld University
2001-2006
In Rd, for any dimension d⩾1, expansions of self‐intersection local times fractional Brownian motions with arbitrary Hurst coefficients in (0,1) are presented. The terms Wick powers white noises (corresponding to multiple Wiener integrals), being well‐defined the sense generalized noise functionals.
The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, linear space potentials spanned by measures and Laplace transforms measures, i.e., locally singular well rapidly growing at infinity. Remarkably, all these propagators admit perturbation expansion.
We extend the Clark-Ocone formula to a suitable class of generalized Brownian functionals.As an example we derive representation Donsker's delta function as (limit of) stochastic integral.
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the process being driven by fractional noise. Price return statistics asymptotic behavior are derived from compared data. Deviations Black-Scholes new option pricing formula also obtained
We construct the time evolution of Kawasaki dynamics for a spatial infinite particle system in terms generating functionals. This is carried out by an Ovsjannikov-type result scale Banach spaces, which leads to local (in time) solution. An application this approach Vlasov-type scaling functionals considered as well.
The Mittag-Leffler function $E_α$ being a natural generalization of the exponential function, an infinite-dimensional version fractional Poisson measure would have characteristic functional \[ C_α(ϕ) :=E_α(\int (e^{iϕ(x)}-1)dμ(x)) \] which we prove to fulfill all requirements Bochner-Minlos theorem. identity support this new with ($α=1$) allows development analysis modeled on through combinatorial harmonic configuration spaces. This setting provides, in particular, explicit formulas for...