We introduce a non-linear stochastic filtering technique to track the state of a free curve from image data. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background respectively. We design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-...

—Gaussian processes such as Brownian motion and the Ornstein-Uhlenbeck process have been popular 1 models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. How2 ever, they have drawbacks which limit their utility. Here I describe new, non-Gaussian stochastic differential 3 equation (diffusion) models of quantitative trait evolution. I present gene...

We prove that the solution of the Hudson–Parthasarathy quantum stochastic differential equation in the Fock space coincides with the solution of a symmetric boundary value problem for the Schrödinger equation in the interaction representation generated by the energy operator of the environment. The boundary conditions describe the jumps in the phase and the amplitude of the Fourier transforms o...

Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the majo...

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. Roughly speaking, besides the assumptions for existence and uniqueness of the solution, one only need assume some additional assumptions on diffusion coefficient in order to obtain Large deviation principle for the dis...

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semi-linear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. The characterization is expressed in terms of the almost sure long-time behavior of trajectories of the equation in relation to the stati...

This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space for optimal control of stochastic distributed parameter systems (SDPSs) governed by partial differential equations (SPDEs) subject to both state-dependent and additive stochastic disturbances. First, nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equ...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point x and an endpoint y that belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition semigroup as...

A quantum theory for the Markovian dynamics of an open system under the unsharp observation which is continuous in time, is developed within the CCR stochastic approach. A stochastic classical equation for the posterior evolution of quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Lang...