Update docs/src/catalyst_applications/jump_simulation_performance.md

Co-authored-by: Sam Isaacson <[email protected]>

Author: TorkelE

docs/src/catalyst_applications/jump_simulation_performance.md

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 We have previously described how to perform simulations of stochastic chemical kinetics *chemical reaction network* (CRN) jump process models using e.g. Gillespie's algorithm. These simulations can, however, be highly computationally intensive. Fortunately, there are several ways to increase their performance (thus reducing runtime). Here, we describe various considerations for performant stochastic chemical kinetics simulations, which we will subsequently refer to as jump process simulations. All jump process simulations arising from stochastic chemical kinetics representations of Catalyst models are performed using stochastic simulation algorithms (SSAs) from JumpProcesses.jl. Please see the [JumpProcesses documentation](https://github.com/SciML/JumpProcesses.jl) for a more extensive introduction to the package and the available solvers.
 
 #### Brief (and optional) introduction to jump simulations
-Jump simulations are continuous time, discrete space, simulations (where the system's state, throughout the simulation, are the discrete copy numbers of each species). The system's state changes at discrete time points (in so-called jumps). For CRNs, these jumps correspond to the occurrence of individual reactions. Here, *stochastic chemical kinetics* describes how the reactions are distributed across time. Typically, the frequency of each reaction depends on its *propensity* (which in turn depends on its *rate* and *substrates*). These depend on the state of the system, and must thus be re-computed whenever the system's state changes. Hence, jump simulations' runtimes are heavily dependent on how frequently these propensities must be recomputed.
+Jump processes are continuous-time, discrete-space stochastic processes. Exact realizations of these processes can be generated using Stochastic Simulation Algorithms (SSAs), of which Gillespie's Direct method is one popular choice. In the chemical reaction modeling context the discrete-state variables typically correspond to the integer-valued number of each chemical species at each time. A system's state changes at discrete time points, the jump times, when the amount of one or more species are increased by integer amounts (for example, the creation of a new protein due to translation, or the removal of one protein due to degradation). For CRNs, these jumps correspond to the occurrence of individual reactions. Typically, the frequency of each reaction depends on its *propensity* (which in turn depends on its *rate* and *substrates*). The propensity of a reaction represents its rate law, i.e. probability per time that it occurs (also known as the associated jump process' intensity function). For example, the reaction `k, A + B --> C + D` has a propensity of $k*A(t)*B(t)$ at time $t$. See [Reaction rate laws used in simulations](@ref) for more details of what propensity function Catalyst generates for a given stochastic chemical kinetics reaction.
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+The time of the next occurrence of some reaction, and the type of reaction that occurs, are sampled from distributions that depend on the current values of the propensity. As the latter depend on the state of the system, they must be recomputed whenever the system's state changes (for example due to a reaction occurring). Hence, jump simulations' run-times are heavily dependent on how frequently these propensities must be recomputed, and how many must be recomputed when a reaction occurs.
 
 Typically, propensities are recomputed only whenever a jump occurs. This means that jump simulations' runtimes, very roughly, scale with the number of jumps. Runtimes typically become prohibitively expensive for:
 - Simulations of large models (either with many different species or where some species occur in large copy numbers).