Algebraic polynomials and moments of stochastic integrals

Algebraic polynomials and moments of stochastic integrals

Moments of Poisson stochastic integrals with random integrands

Extreme value theory for stochastic integrals of Legendre polynomials

For t ≥ 0, let X(t) = (X0(t), . . . , Xp(t)) , where Xi(t) denotes the integral of the ith order Legendre polyonimal with respect to the same Brownian motion described by the corresponding standard deviation (0 ≤ i ≤ p). We obtain the exact tail behavior of P ( sup0≤t≤h |X(t)| > u ) as u → ∞, and the limit distribution of sup0≤t≤T |X(t)| as T → ∞. These processes naturally arise in the context ...

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

The moments of stochastic integrals and the distribution of sojourn times.

For a single diallelic locus in a finite population with any time-independent selection scheme, using the diffusion approximation, a formula is derived in terms of sojourn times for the moments of the integral of an arbitrary function of gene frequency along sample paths. Irreversible mutation and conditioned and unconditioned processes without mutation are treated. From this expression, the di...