# Jump Problem and Jump Diffusion Solvers

`solve(prob::JumpProblem,alg;kwargs)`

## Recommended Methods

A `JumpProblem(prob,aggregator,jumps...)`

come 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 equations, use the same methods as in the case of the differential equation solving. However, the following algorithms are optimized for pure jump problems.

### JumpProcesses.jl

`SSAStepper`

: a stepping algorithm for pure`ConstantRateJump`

and/or`MassActionJump`

`JumpProblem`

s. 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.

### JumpProcesses.jl

`SimpleTauLeaping`

: a tau-leaping algorithm for pure`RegularJump`

`JumpProblem`

s. Requires a choice of`dt`

.`RegularSSA`

: a version of SSA for pure`RegularJump`

`JumpProblem`

s.

## Regular Jump Diffusion Compatible Methods

Regular jump diffusions are `JumpProblem`

s 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.