The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index H > 1/2 can be estimated by O(δ) (δ is the diameter of partition). For discrete-time approximations of Sko...

A Stochastic Differential Equation (SDE) appearing in mathematical finance is considered in random environment by assuming that its two parameters are switched by an unobserved continuous-time Markov chain whose states represent the states of the market environment. A Dirichlet process is placed as a prior on the space of the sample paths ∗corresponding author:[email protected]...

We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an R-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show th...

We consider conditional McKean–Vlasov stochastic differential equations (SDEs), as the ones arising in large-system limit of mean field games and particle systems with interactions when common noise is present. The time-marginals solutions to these SDEs are governed by non-linear partial (SPDEs) second order, whereas their laws satisfy Fokker–Planck on space probability measures. Our paper esta...

This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). SIR is proposed and under different intervals HAM to obtain numerical solution of Furthermore, ODE was transformed into a stochastic differential equation (SDE) results deterministic models were compared using s...

We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itôtype equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of inva...

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic differential equation (SDE) descriptions realistically-sampled time series data, to understand Kuramoto model coupled oscillators. find across entire bifurcati...

In this paper we use the analogy of Parrondo's games to design a second order switched mode circuit which is unstable in either mode but is stable when switched. We do not require any sophisticated control law. The circuit is stable, even if it is switched at random. We use a stochastic form of Lyapunov's second method to prove that the randomly switched system is stable with probability of one...

We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (a...

Abstract. It is known that reversible Langevin diffusions in confining potentials converge to equilibrium exponentially fast. Adding a divergence free component to the drift of a Langevin diffusion accelerates its convergence to stationarity. However such a stochastic differential equation (SDE) is no longer reversible. In this paper, we analyze the optimal scaling of MCMC algorithms constructe...