Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming

DOI10.1137/16M107801XzbMath1355.60106arXiv1606.01153MaRDI QIDQ2953227

Michela Ottobre, Juan Kuntz, Mauricio Barahona, Guy-Bart Stan

Publication date: 4 January 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.01153

zbMATH Keywords

semidefinite programmingstochastic differential equationsLyapunov exponentsmoment problemsstationary measurespolynomial diffusions

Mathematics Subject Classification ID

Semidefinite programming (90C22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (9)

Moment and polynomial bounds for ruin-related quantities in risk theory ⋮ Convex computation of maximal Lyapunov exponents ⋮ Auxiliary functions as Koopman observables: data-driven analysis of dynamical systems via polynomial optimization ⋮ Tighter bounds on transient moments of stochastic chemical systems ⋮ Stationary Distributions of Continuous-Time Markov Chains: A Review of Theory and Truncation-Based Approximations ⋮ Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization ⋮ Moment analysis of stochastic hybrid systems using semidefinite programming ⋮ Finding Extremal Periodic Orbits with Polynomial Optimization, with Application to a Nine-Mode Model of Shear Flow ⋮ Bounding Extreme Events in Nonlinear Dynamics Using Convex Optimization

Uses Software

• SDPT3
• GloptiPoly
• SeDuMi Interface

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An optimization approach to weak approximation of stochastic differential equations with jumps
• Extremes and related properties of random sequences and processes
• Qualitative behavior of geostochastic systems
• Random differential equations in science and engineering
• Exponential convergence of Langevin distributions and their discrete approximations
• Semidefinite programming relaxations for semialgebraic problems
• Numerical comparison of controls and verification of optimality for stochastic control problems
• Markov chains and invariant probabilities
• Bounds on measures satisfying moment conditions.
• Stability of regime-switching stochastic differential equations
• Hypoelliptic second order differential equations
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• A LINEAR PROGRAMMING APPROACH TO THE STEADY-STATE ANALYSIS OF REFLECTED BROWNIAN MOTION
• Inverse problems: A Bayesian perspective
• METHOD OF MOMENTS APPROACH TO PRICING DOUBLE BARRIER CONTRACTS IN POLYNOMIAL JUMP-DIFFUSION MODELS
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• SDP vs. LP Relaxations for the Moment Approach in Some Performance Evaluation Problems
• GloptiPoly 3: moments, optimization and semidefinite programming
• Second-order discretization schemes of stochastic differential systems for the computation of the invariant law
• Bounding Stationary Expectations of Markov Processes
• Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming
• Approximation of Upper Lyapunov Exponents of Bilinear Stochastic Differential Systems
• Lyapunov Exponents and Stochastic Stability of Coupled Linear Systems Under Real Noise Excitation
• Foundations of Modern Probability
• SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
• Extension Of Dale's Moment Conditions With Application To The Wright–fisher Model
• On Weak Approximation of Stochastic Differential Equations through Hard Bounds by Mathematical Programming
• Ergodic Properties of Markov Processes
• Statistical Behavior of Linear Systems with Randomly Varying Parameters
• PRICING A CLASS OF EXOTIC OPTIONS VIA MOMENTS AND SDP RELAXATIONS

This page was built for publication: Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming