We consider a stochastic Camassa-Holm equation driven by one-dimensional Wiener process with first order differential operator as diffusion coefficient. prove the existence and uniqueness of local strong solutions this equation. In to do so, we transform it into random quasi-linear partial apply Kato's theory methods. Some results have potential find applications other nonlinear equations.

We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solut...

in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...

We perform and compare different analyses of triply degenerate four-wave mixing in the regime where three fields of the same frequency interact via a nonlinear medium with a field at three times the frequency. As the generalized Fokker-Planck equation ~GFPE! for the positive-P function of this system contains third-order derivatives, there is no mapping onto genuine stochastic differential equa...

We extend the narrowband Weyl symbol (WS) and the wideband P0-Weyl symbol (P0WS) for dispersive time–frequency (TF) analysis of nonstationary random processes and time-varying systems. We obtain the new TF symbols using unitary transformations on the WS and the P0WS. For example, whereas the WS is matched to systems with constant or linear TF characteristics, the new symbols are better matched ...

A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation" completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of t...