Linear-implicit versions of strong Taylor numerical schemes for finite dimensional It6 stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an 7 strong linear-implicit Taylor scheme with time-step A applied to the N dimensional It6-Galerkin SDE for a class of parabolic stochastic partial diff...

In our ongoing work, we aim to control a team of agents so as to achieve a prescribed goal state while being confident that collisions with other agents are avoided. Each agent is associated with a feedback controlled plant, whose continuous state trajectories follow some stochastic differential dynamics. To this end we describe a collision-detection module based on a distribution-independent p...

In this paper we examine the cumulant properties of generally multiplicative noise of stochastically equivalent stochastic differential equations (SDE) for a given (integro) master equation. For an I to-SDE we obtain as a necessary consequence that the noise f i ( t ) possesses a ~-correlated 2-nd order conditioned cumulant ( f l ( t l ) f i ( t 2 ) l x ( t * ) = x ) if t* < max {t 2, t~ }. For...

The First-Passage Time (FPT) problems have numerous practical applications in fields that go from engineering and physics to finance and biology among many others. For the case of Markov gamma processes, this paper develops a methodology that combines the first Pontryagin equation approach and the cumulant analysis in order to obtain FPT statistics. For investigation about the structure of the ...

A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to...

Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians a discrete form of version Dirichlet energy, signifying relationship the Harmonic map heat flow equation. The Gibbs distribution, defined with this Hamiltonian, is Metropolis-Hastings (M-H) algorithm generate dynamics tending towards an equilibrium state. In limiting situation when inverse temperatur...

We present the computation of massless three-loop ladder-box family with one external off-shell leg using Simplified Differential Equations (SDE) approach. also discuss methods we used for finding a canonical differential equation two tennis-court families leg, and application SDE approach on these families.

A simulation based method for the numerical solution of PDEs with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead t...

We present an extension of the variational Bayesian nonlinear state-space model introduced by Valpola and Karhunen in 2002 [1] for continuous-time models. The model is based on using multilayer perceptron (MLP) networks to model the nonlinearities. Moving to continuous-time requires solving a stochastic differential equation (SDE) to evaluate the predictive distribution of the states, but other...

Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed. Different interpretations specify different dynamics. Recently, a new interpretation of SDE is put forward by one of us. This interpretation has a built-in Boltzmann...