相关论文: On the Interpretation of Stratonovich Calculus

We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not…

In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize $\alpha>0$. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new…

Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…

We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows one to systematically develop low dimensional approximations to high dimensional…

In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic…

We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich…

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…

Since the seminal work of Wiener, the chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations. Yet its complexity for systems subject to the white noise remains significant. The…

We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…

We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…

Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important…

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…

In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a…

In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…

We study equations like the Mackey-Glass equations and Nicholson's blowflies equation, each perturbed by a (small) multiplicative noise term. Solutions to these stochastic negative feedback systems persist globally and are bounded above in…

Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is driven by finite-time excursions rather…

We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative It\^o and Stratonovich noise, and transport noise. We…

We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to…