Multi‐valued backward stochastic differential equations driven by G‐Brownian motion and its applications
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4335
Abstract: In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover,… read more here.
Keywords: stochastic differential; backward stochastic; brownian motion; equations driven ... See more keywords
Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Robust and Nonlinear Control"
DOI: 10.1002/rnc.5764
Abstract: This article is concerned with exponential mean square stabilization of stochastic systems driven by fractional Brownian motion subject to state‐delay and uncertainties by sliding mode control. By applying the proposed method, the states of the… read more here.
Keywords: square exponential; fractional brownian; stochastic systems; mean square ... See more keywords
The Zero Set of Fractional Brownian Motion Is a Salem Set
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-017-9551-9
Abstract: The existence of sets supporting a Borel measure such that its Fourier transform tends to zero at infinity can be traced back to the problem of uniqueness of trigonometric series, studied extensively by Cantor. Given… read more here.
Keywords: brownian motion; salem sets; fractional brownian; motion salem ... See more keywords
Sample Paths Estimates for Stochastic Fast-Slow Systems Driven by Fractional Brownian Motion
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-020-02485-4
Abstract: We analyze the effect of additive fractional noise with Hurst parameter $$H > {1}/{2}$$ H > 1 / 2 on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by… read more here.
Keywords: fast slow; sample paths; paths estimates; slow systems ... See more keywords
A New Model of Campi Flegrei Inflation and Deflation Episodes Based on Brownian Motion Driven by the Telegraph Process
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Geosciences"
DOI: 10.1007/s11004-018-9756-8
Abstract: A stochastic model to describe the vertical motions in the Campi Flegrei volcanic region is proposed herein, consisting of a Brownian motion process driven by a generalized telegraph process. Knowledge on the probability law of… read more here.
Keywords: campi flegrei; process; brownian motion; model ... See more keywords
An Efficient Algorithm for Simulating the Drawdown Stopping Time and the Running Maximum of a Brownian Motion
Sign Up to like & getrecommendations! Published in 2017 at "Methodology and Computing in Applied Probability"
DOI: 10.1007/s11009-017-9542-y
Abstract: We define the drawdown stopping time of a Brownian motion as the first time its drawdown reaches a duration of length 1. In this paper, we propose an efficient algorithm to efficiently simulate the drawdown… read more here.
Keywords: drawdown stopping; time; brownian motion; efficient algorithm ... See more keywords
First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries
Sign Up to like & getrecommendations! Published in 2019 at "Methodology and Computing in Applied Probability"
DOI: 10.1007/s11009-018-9638-z
Abstract: Explicit formulas for the first hitting time distributions for a standard Brownian motion and different regions including rectangular, triangle, quadrilateral and a region with piecewise linear boundaries are derived. Moreover, approximations to the first hitting… read more here.
Keywords: hitting time; linear boundaries; time distributions; brownian motion ... See more keywords
Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators
Sign Up to like & getrecommendations! Published in 2019 at "Methodology and Computing in Applied Probability"
DOI: 10.1007/s11009-018-9648-x
Abstract: In recent years subordinated processes have been widely considered in the literature. These processes not only have wide applications but also have interesting theoretical properties. In this paper we consider fractional Brownian motion (FBM) time-changed… read more here.
Keywords: tempered stable; inverse tempered; fractional brownian; motion delayed ... See more keywords
Numerical methods for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion
Sign Up to like & getrecommendations! Published in 2019 at "Numerical Algorithms"
DOI: 10.1007/s11075-019-00800-z
Abstract: In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion. The main challenges of the numerical schemes come from the singularity… read more here.
Keywords: planck equation; fokker planck; tempered fractional; fractional brownian ... See more keywords
An M-estimator for stochastic differential equations driven by fractional Brownian motion with small Hurst parameter
Sign Up to like & getrecommendations! Published in 2020 at "Statistical Inference for Stochastic Processes"
DOI: 10.1007/s11203-020-09214-4
Abstract: Let us consider a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $$1/4< H < 1/2$$ 1 / 4 < H < 1 / 2 . We are interested in estimating… read more here.
Keywords: fractional brownian; stochastic differential; driven fractional; brownian motion ... See more keywords
Supercritical branching Brownian motion with catalytic branching at the origin
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DOI: 10.1007/s11425-017-9267-7
Abstract: We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β > 0 on the local time scale. We first establish a… read more here.
Keywords: branching brownian; branching; catalytic branching; brownian motion ... See more keywords