Related papers: Neural Brownian Motion
In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on the martingale part $M$ of a solution. We assume that the nonlinear term is merely monotone…
Anomalous transport of non-Markovian, thermal Brownian particle dynamics in spatially-periodic symmetric systems that is driven by time-periodic symmetric driving and constant bias is investigated numerically. The Brownian dynamics is…
We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…
We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a…
We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift…
In this paper, we introduce and analyze the fractional Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. The proposed model is based upon two desirable properties of the long-term variance process suggested by the empirical…
In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a…
During training, weight matrices in machine learning architectures are updated using stochastic gradient descent or variations thereof. In this contribution we employ concepts of random matrix theory to analyse the resulting stochastic…
We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical stochastic multiplicative process for non-stationary and non-ergodic dynamics. Resetting is a sudden interruption of a process, which consecutively…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
The $N$-particle branching Brownian motion ($N$-BBM) is a branching Markov process which describes the evolution of a population of particles undergoing reproduction and selection. It has attracted a lot of interest due to its relations to…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
This paper discusses a new type of anticipated backward stochastic differential equation with a time-delayed generator (DABSDEs, for short) driven by fractional Brownian motion, also known as fractional BSDEs, with Hurst parameter…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…
Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance,…
Building upon our prior work [1], we present a unified stochastic drift model (SdM) for superconducting charge qubits based on memory multi-fractional Brownian motion (mmFBM). The classical sector employs a time-dependent Hurst exponent…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
This paper deals with a projection least squares estimator of the function $J_0$ computed from multiple independent observations on $[0,T]$ of the process $Z$ defined by $dZ_t = J_0(t)d\langle M\rangle_t + dM_t$, where $M$ is a continuous…