Fractional Langevin Monte Carlo: Exploring Lévy Driven Stochastic Differential Equations for MCMCSUPPLEMENTARY DOCUMENT

Fractional Langevin Monte Carlo: Exploring Levy Driven Stochastic Differential Equations for Markov Chain Monte Carlo

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based on diffusions driven by a Brownian motion, which gives rise to Gaussian proposal distributions in the resulting algorithms. Even though these approaches hav...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Fractional Lévy driven Ornstein-Uhlenbeck processes and stochastic differential equations

Using Riemann-Stieltjes methods for integrators of bounded p-variation we define a pathwise integral driven by a fractional Lévy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper inte...

A Monte Carlo EM algorithm for discretely observed Diffusions, Jump-diffusions and Lévy-driven Stochastic Differential Equations

Stochastic differential equations driven by standard Brownian motion(s) or Lévy processes are by far the most popular models in mathematical finance, but are also frequently used in engineering and science. A key feature of the class of models is that the parameters are easy to interpret for anyone working with ordinary differential equations, making connections between statistics and other sci...

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...