A new kind of backward stochastic differential equations (in short BSDE), where the solution is a pair of processes adapted to the past of the driving Brownian motion, has been introduced by the authors in [63. It was then shown in a series of papers by the second and both authors (see [8, 7, 9, 103), that this kind of backward SDEs gives a probabilistic representation for the solution of a lar...

In this paper, we discuss the Banach fixed point theorem conditions on optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. respect, consider integral representation which is extracted as a consequence Feynman-Kac formula. order prove above features, define nonempty closed set in space...

We present a non asymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L2relative error of these weigh...

Let X be a symmetric right process, and let Z = {Zt, t ≥ 0} be a multiplicative functional of X that is the product of a Girsanov transform, a Girsanov transform under time-reversal and a continuous Feynman-Kac transform. In this paper we derive necessary and sufficient conditions for the strong L-continuity of the semigroup {Tt, t ≥ 0} given by Ttf(x) = Ex [Ztf(Xt)], expressed in terms of the ...

The Feynman-Kac formula implies that every suitable classical solution of a semilinear Kolmogorov partial differential equation (PDE) is also certain stochastic fixed point (SFPE). In this article we study such and related SFPEs. particular, the main result work proves existence unique solutions SFPEs in general setting. As an application establish associated with PDEs Lipschitz continuous nonl...

<p style='text-indent:20px;'>We consider the cooperative system driven by a multiplicative It\^o type white noise. The existence and their approximations of travelling wave solutions are proven. With moderately strong noise, constricted choosing suitable marker wavefront. Moreover, stochastic Feynman-Kac formula, sup-solution, sub-solution equilibrium points dynamical corresponding to uti...