Approximate solution for some stochastic differential equations involving both Gaussian and Poissonian white noises (Q1433190)

This paper derives a stochastic differential equation involving fractional Brownian motion whose solution approximates the solution of the stochastic differential equation \[ {dx(t)\over dt}= f(x)+ g(x) w(t)+ h(x) v(t),\quad x(t_0)= x_0, \] where \(w(t)\) is normalized Gaussian white noise and \(v(t)= \sum^{N(t)}_{j=1} z_j\delta(t- t_j),\) where \(N(t)\) is a Poisson process and \(z_1,z_2,\dots\) is a sequence of independent, identically distributed random variables. An example is given in which this approach is applied to an equation encountered in finance.