We present the stochastic approach to nonlinear kinetic
equations (without gradient terms) in a unifying general
framework, which covers many interactions important in
applications, such as
coagulation, fragmentation, inelastic collisions, as well as
source and efflux terms. We provide conditions for the
existence of corresponding stochastic particle systems
in the sense of regularity (nonexplosion) of a jump process
with unbounded intensity. Using an appropriate space of measure-valued
functions, we prove relative compactness of the
sequence of processes and characterize the weak limits in terms of solutions
to the nonlinear equation. As a particular application, we derive
existence theorems for Smoluchowski's coagulation equation
with fragmentation, efflux and source terms, and for the Boltzmann
equation with inelastic collisions.