Sampling conditioned diffusions via Pathspace Projected Monte Carlo

TL;DR

This paper introduces a novel pathspace Monte Carlo algorithm for sampling stochastic differential equations under various complex constraints, enabling efficient exploration of conditioned stochastic processes.

Contribution

The paper proposes a new manifold sampling scheme that effectively handles general conditioning constraints in stochastic differential equations.

Findings

Successfully sampled a dynamical condensation phase transition.

Conditioned a random walk on a fixed Levy stochastic area.

Sampled a stochastic nonlinear wave equation conditioned on high amplitude waves.

Abstract

We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that adhere to the conditioning constraint. We demonstrate the effectiveness of the algorithm by sampling a dynamical condensation phase transition, conditioning a random walk on a fixed Levy stochastic area, conditioning a stochastic nonlinear wave equation on high amplitude waves, and sampling a stochastic partial differential equation model of turbulent pipe flow conditioned on relaminarization events.