A poly-disperse particle description using a Lagrangian Stochastic (LS) framework coupled to Large Eddy Simulations (LES) of turbulent flows is presented. The aforementioned frameworks are outlined leading to the LES-coupled spray-pdf equation and its equivalent Stochastic Differential Equations (SDE). Three particle processes are investigated: particle dispersion, nucleation and aggregation. The aim of this work is to integrate or extend the models of these processes into the LES-LS framework and evaluate the predictive ability of the developed models. Dispersion in LES is used in conjunction with a stochastic sub-grid model to accurately represent the path of a particle. Such models have a free parameter, the dispersion coefficient, which is not universal. A dynamic model for the evaluation of this coefficient is proposed. The model's predictive ability is investigated in decaying homogeneous isotropic turbulence and a turbulent mixing layer. Nucleation is modelled in a probabilistic manner where the frequency of events is determined from local equilibrium conditions. Two methodologies for the sub-grid influence on nucleation rates are implemented. A turbulent Dibutyl-Phthalate laden Nitrogen jet experiment is used for validation. Aggregation is an inter-particle process which involves a multitude of different physicochemical mechanisms. Particles in the nano-scale are considered, with a concentration which renders their direct simulation as individual real particles intractable. A stochastic aggregation model is presented and its performance is evaluated against analytic solutions, a Planar Jet, and a turbulent jet configuration. It is concluded that the LES-spray pdf framework can be used to develop parameter-free models from phenomenological arguments that accurately describe complex turbulent poly-disperse flows.