R/prony_coeff.R
prony_coeff.RdCoefficients of position-process representation of the Prony-GLE.
prony_coeff(lambda, nu, r, C, nsteps = 100, tol = 0)Vector of length K giving the inverse decorrelation times of the exponential decay terms.
Autocorrelation scaling factor.
Optional vector of pre-computed OU mean-reversion parameters. Avoids calling the mode-finding routine.
Optional vector of pre-computed OU scale coefficients. Can't pass C without r. When both r and C are supplied the function does nothign. This is mainly for the convenience of calling prony_coeff() from other functions.
Number of steps in mode-finding golden search algorithm.
Relative tolerance in mode-finding golden search algorithm. For numerical stability, default is 0 such that nsteps are always used.
A list with elements r and C, containing the length(lambda)-1 and length(lambda) vectors of mean-reversion parameters and scale factors for the BM + OU representation of the Prony-GLE.
The Prony-GLE model satisfies the integro-differential equation $$ F_t - \int_{-\infty}^t \kappa(t-s) \dot X_s ds = 0, \qquad ACF_F(t) = k_B T \kappa(t), $$ where \(T\) is temperature, \(k_B\) is Boltzmann's constant, and the memory kernel is a sum of exponentials: $$ \kappa(t) = \nu sum_{k=1}^K exp(-\lambda_k t). $$ The solution process is of the form $$ X_t = C_0 B_t + \sum_{i=1}^{K-1} C_i W_{it}, $$ where \(B_t\) is Brownian motion and \(d W_{it} = -\rho_i W_{it} dt + d B_{it}\) are Ornstein-Uhlenbeck processes all independent of each other and of \(B_t\).
Since temperature is not provide, C is only proportional to the true vector C_true, such that C_true = sqrt(k_B T) * C.