Recently, a new approach in the fine analysis of sample paths of stochastic processes has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved...

In this paper, we establish an equivalence relationship between the wellposedness of forward–backward SDEs (FBSDEs) with random coefficients and that of backward stochastic PDEs (BSPDEs). Using the notion of the “decoupling random field”, originally observed in the well-known Four Step...

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our aim is to quantify the amount of information the...

The contribution of this paper is twofold: we study power utility maximization problems (with and without intermediate consumption) in a partially observed financial market with jumps and we solve by the innovation method the arising filtering problem. We consider a Markovian model where the...

Parametric estimation of two-dimensional hypoelliptic diffusions is considered when complete observations–both coordinates discretely observed–or partial observations–only one coordinate observed–are available. Since the volatility matrix is degenerate, Euler contrast estimators cannot...

We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in a dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being advected by a stochastic Stokes fluid velocity field....