Random ideas: stochastic calculus and more

Multidimensional exponential timestepping with boundary test

Exponential timestepping algorithms are efficient for exit-time problems because a boundary test can be performed at the end of each timestep, giving high-order convergence in numerical evaluation of mean exit times. Successive time increments are independent random variables with an exponential distribution. In the figure on the right, one realization is depicted. Exponential timesteps are jumps from one black point to the next. The values of the process at these times are generated, but not the corresponding times.
Downloadable programs: Timestepping with boundary test
Exit from Circle Circle.c  Circle2.c
Exit from Sphere Sphere.c
Exit from Ellipse Ellipse2D.c
Exit from concave region Hyp.c  Hyp2.c
Header file MySignals.h

Exponential timestepping with boundary test for scalar stochastic differential equations

Kalvis Jansons and Grant Lythe       SIAM Journal on Scientific Computing   24  1809  (2003)

Efficient numerical solution of stochastic differential equations using exponential timestepping

Kalvis Jansons and Grant Lythe       Journal of Statistical Physics   100    1097 (2000)

Downloadable programs in: C FORTRAN90 / HPF
Basic timestepping Exp01.c Expdw01.f   eeF90.in
Timestepping with boundary test Expb01.c Expbdw01.f   dwb.in

Other work

Stochastic Stokes' drift

Kalvis Jansons and Grant Lythe       Physical Review Letters   81  3136-3139   (1998)

Please note: On some web sites, the author list for the above paper appears differently. The correct author list, in spelling and in alphabetical order, is as above and any different versions are incorrect, and should be ignored.

Stochastic calculus: application to dynamic bifurcations and threshold crossings

Kalvis Jansons and Grant Lythe       Journal of Statistical Physics  90  227-251  (1998)
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