Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations
A variable step size method for the numerical approximation of pathwise solutions to stochastic differential equations (SDEs) and its dependence on a representation of Bro...
Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations
The extent to which this order of convergence can be improved is investigated, and it is found that better approximations are possible for the case of additive noise, but for multiplicative noise it is shown that no improvements are possible.
Random Generation of Stochastic Area Integrals
A method of random generation of the integrals based on Marsaglia's “rectangle-wedge-tail” method for simulation of strong solutions of general multidimensional stochastic differential equations with an order of convergence better than $O( h )$ in the general case.
The algebra of iterated stochastic integrals
- J. Gaines
- 1 August 1994
Using results from work on shuffle algebras, we show that Lyndon words provide an algebraic basis for the sets of iterated Stratonovich or Ito integrals that appear in the stochastic Taylor series…
An efficient approximation method for stochastic differential equations by means of the exponential Lie series
Convergence of a Branching Particle Method to the Solution of the Zakai Equation
A sequence of branching particle systems Un convergent in distribution to the solution of the Zakai equation is constructed, which can be used to solve numerically the filtering problem.
The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
Nous nous interessons aux approximations numeriques des solutions fortes d'une equation differentielle stochastique (EDS), utilisant un pas de temps fixe, et les increments de la trajectoire…
Stochastic Partial Differential Equations: Numerical experiments with S(P)DE's
- J. Gaines
A basis for iterated stochastic integrals
- J. Gaines
- 1 May 1995
Approximate travelling waves for generalized KPP equations and classical mechanics
- K. Elworthy, A. Truman, Huaizhong Zhao, J. Gaines
- MathematicsProceedings of the Royal Society of London…
- 8 September 1994
We consider the existence of approximate travelling waves of generalized KPP equations in which the initial distribution can depend on a small parameter μ which in the limit μ → 0 is the sum of some…