# Jump Problem and Jump Diffusion Solvers

solve(prob::JumpProblem,alg;kwargs)

A JumpProblem(prob,aggregator,jumps...) comes in two forms. The first major form is if it does not have a RegularJump. In this case, it can be solved with any integrator on prob. However, in the case of a pure JumpProblem (a JumpProblem over a DiscreteProblem), there are special algorithms available. The SSAStepper() is an efficient streamlined algorithm for running the aggregator version of the SSA for pure ConstantRateJump and/or MassActionJump problems. However, it is not compatible with event handling. If events are necessary, then FunctionMap does well.

If there is a RegularJump, then specific methods must be used. The current recommended method is TauLeaping if you need adaptivity, events, etc. If you just need the most barebones fixed time step leaping method, then SimpleTauLeaping can have performance benefits.

## Special Methods for Pure Jump Problems

If you are using jumps with a differential equation, use the same methods as in the case of the differential equation solving. However, the following algorithms are optimized for pure jump problems.

### DiffEqJump.jl

• SSAStepper: a stepping algorithm for pure ConstantRateJump and/or MassActionJump JumpProblems. Supports handling of DiscreteCallback and saving controls like saveat.

## RegularJump Compatible Methods

### StochasticDiffEq.jl

These methods support mixing with event handling, other jump types, and all of the features of the normal differential equation solvers.

• TauLeaping: an adaptive tau-leaping algorithm with post-leap estimates.

### DiffEqJump.jl

• SimpleTauLeaping: a tau-leaping algorithm for pure RegularJump JumpProblems. Requires a choice of dt.
• RegularSSA: a version of SSA for pure RegularJump JumpProblems.

## Regular Jump Diffusion Compatible Methods

Regular jump diffusions are JumpProblems where the internal problem is an SDEProblem and the jump process has designed a regular jump.

### StochasticDiffEq.jl

• EM: Explicit Euler-Maruyama.
• ImplicitEM: Implicit Euler-Maruyama. See the SDE solvers page for more details.