Results 11 to 20 of about 21,651 (169)
Mathematics, 2021 The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention,
Siow Woon Jeng, Adem Kiliçman
doaj +1 more source
ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS [PDF]
Stochastics and Dynamics, 2009 In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that contains backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations.
openaire +3 more sources
Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients [PDF]
Foundations of Computational Mathematics, 2011 Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case of superlinearly growing coefficients, however, has remained an open question. The main difficulty is
Hutzenthaler, Martin, Jentzen, Arnulf
openaire +2 more sources
Stochastic flows for SDEs with non-Lipschitz coefficients
Bulletin des Sciences Mathématiques, 2003 A stochastic differential equation \[ dX_t=\sum_{n=1}^\infty\sigma_n(X_t)dW_t^n+b(X_t)dt,\quad X_0=x\in{\mathbb R}, \] is considered, where \(W^n\) are Brownian motions, \(n=1,2,\dots\), and none of the \(\sigma_n\)'s or \(b\) are Lipschitz. Conditions on coefficients are given which imply that the solution is a.s.\ continuous in \(x\) and \(t\) for ...
Ren, Jiagang, Zhang, Xicheng
openaire +1 more source
Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient
Mathematics, 2020 We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient.
Kęstutis Kubilius, Aidas Medžiūnas
doaj +1 more source
A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient [PDF]
, 2006 The existence of a mean-square continuous strong solution is established for vector-valued Itö stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion ...
Halidias, Nikolaos, Kloeden, Peter E.
core +3 more sources
Anticipated Backward Doubly Stochastic Differential Equations with Non-Lipschitz Coefficients [PDF]
Mathematics, 2022 The work presented in this paper focuses on a type of differential equations called anticipated backward doubly stochastic differential equations (ABDSDEs) whose generators not only depend on the anticipated terms of the solution (Y·,Z·) but also satisfy one kind of non-Lipschitz assumption.
Tie Wang, Siyu Cui
openaire +2 more sources
Generalized Stochastic Burgers' Equation with Non-Lipschitz Diffusion Coefficient
Communications on Stochastic Analysis, 2019 Summary: We study the existence of weak solutions to the one-dimensional generalized stochastic Burgers' equation with polynomial nonlinearity perturbed by space-time white noise with Dirichlet boundary conditions and \(\alpha\)-Hölder continuous coefficient in noise term, where \(\alpha\in[1/2,1)\).
Kumar, Vivek, Giri, Ankik Kumar
openaire +2 more sources
Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient [PDF]
, 2018 We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.
Leobacher, Gunther +1 more
core +2 more sources
Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients
AIMS Mathematics, 2020 In the paper, the following stochastic differential equation \[ d X(t) = f(X(t),i)dt+g(X(t),i)dw(t), \quad 1\leq i\leq N, \tag{1} \] with the initial condition \[ \qquad X(0)= x\in \mathbb{R}^{d} \tag{2} \] is considered. In (1)-(2), \(\mathcal{M}=\left\{ 1,2,3,\ldots,N \right\}\), \(f:\mathbb{R}^{d}\times\mathcal{M}\to \mathbb{R}^{d}\) and \(g:\mathbb{
Chunhong Li, Sanxing Liu
openaire +2 more sources