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Existence of random dynamical systems for a class of coalescing stochastic flows on ℝ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential equations and coalescing Harris flows are considered. [ABSTRACT FROM AUTHOR]

This paper presents a probabilistic interpretation for the weak Sobolev solution of the obstacle problem for semilinear parabolic partial integro-differential equations (PIDEs). The results of Léandre [32] concerning the homeomorphic property for the solution of SDEs with jumps are used to construct random test functions for the variational equation for such PIDEs. This results in the natural connection with the associated Reflected Backward Stochastic Differential Equations with jumps (RBSDEs), namely Feynman-Kac's formula for the solution of the PIDEs. Moreover, it gives an application to the pricing and hedging of contingent claims with constraints in the wealth or portfolio processes in financial markets including jumps. [ABSTRACT FROM AUTHOR]

A natural "flow" over super-Brownian motions, which is not in Le Jan-Raimond framework on stochastic flows of measurable maps and kernels, is discovered in this paper. [ABSTRACT FROM AUTHOR]

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment. [ABSTRACT FROM AUTHOR]

In this paper we study how σ-finite measures on ℝd evolve under a class of "stochastic flows" associated to stochastic differential equations with (resp. without) jumps in ℝd. First we show the related measure evolution processes are càdlàg (resp. continuous), strongly Markovian and weakly Fellerian. Then we extend the existing results on incompressibility in Harris [8] and Kunita [14], and prove strong Markov property of the process describing how compact subsets evolve under incompressible "stochastic flows" under a certain condition. [ABSTRACT FROM AUTHOR]

In many physical applications it is important to predict particle trajectories in a turbulent flow using a numerical model of the flow. One of the major reasons for a poor prediction is the limited resolution in space. We discuss the problem of predictability limits in the framework of a stochastic flow modeling inertial particles in turbulence. Two stochastic flows called the "model" and "true" are considered. The "model" flow is the "true" flow smoothed in space. The principal measure of discrepancy of the flows is the distance between the centers of mass of two initially identical particle clusters driven by the "true" and "model" flows respectively. The predictability limit is defined as a moment when this distance exceeds the space correlation scale of the true flow. The main result is a simple formula relating the predictability limit with the smoothing scale. This relation is well supported by stochastic simulations and could be a helpful tool in planning experiments in numerical models of turbulent flows. Also the difference between particle scattering in the "true" and "model" flows is studied. [ABSTRACT FROM AUTHOR]