Exact simulation of nonlinear coagulation processes

Exact simulation of nonlinear coagulation processes

The Smoluchowski equation is a nonlinear integro-differential equation describing the evolution of the concentration μt(dx) of particles of mass in (x, x+ dx) in an infinite particle system where coalescence occurs. We introduce a class of algorithms, which allow, under some conditions, to simulate exactly a stochastic process (Xt)t≥0, whose time marginals are given by (xμt(dx))t≥0.

Exact Simulation of Time-Varying Fractionally Differenced Processes

Time-varying fractionally differenced (TVFD) processes can serve as useful models for certain time series whose statistical properties evolve over time. A TVFD process can be taken to have a spectral density function that obeys a power law at low frequencies with a time-varying exponent. In contrast to locally stationary or locally self-similar processes, the power law exponent for a TVFD proce...

Exact Simulation of Point Processes with Stochastic Intensities

Point processes with stochastic intensities are ubiquitous in many application areas, including finance, insurance, reliability and queuing. They can be simulated from a standard Poisson process by time-scaling with the cumulative intensity, or compensator. The paths of the compensator are often generated with a discretization method. However, discretization introduces bias into the simulation ...

Exact Simulation of Time-Varying Fractionally Differenced Processes

Time-varying fractionally differenced (TVFD) processes can serve as useful models for certain time series whose statistical properties evolve over time. The spectral density function for a TVFD process obeys a power law whose exponent can be time dependent. In contrast to locally stationary or locally self-similar processes, the power law exponent for a TVFD process is not restricted to certain...

Exact solutions of nonlinear interval Volterra integral equations