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   Articles with "stochastic volterra" as a keyword



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Itô Differential Representation of Singular Stochastic Volterra Integral Equations

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recommendations! Published in 2020 at "Acta Mathematica Scientia"

DOI: 10.1007/s10473-020-0624-5

Abstract: In this paper we obtain an Itô differential representation for a class of singular stochastic Volterra integral equations. As an application, we investigate the rate of convergence in the small time central limit theorem for… read more here.

Keywords: stochastic volterra; differential representation; integral equations; singular stochastic ... See more keywords
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Convergence of the balanced Euler method for a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients

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recommendations! Published in 2020 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2020.03.010

Abstract: Abstract In this paper, we propose the balanced Euler method of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The moment boundedness and strong convergence are shown. Moreover, the theoretical results… read more here.

Keywords: stochastic volterra; balanced euler; method class; class stochastic ... See more keywords
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Wavelets method for solving nonlinear stochastic Itô–Volterra integral equations

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recommendations! Published in 2018 at "Georgian Mathematical Journal"

DOI: 10.1515/gmj-2018-0009

Abstract: Abstract In this paper, a new computational method based on the Chebyshev wavelets (CWs) is proposed for solving nonlinear stochastic Itô–Volterra integral equations. In this way, a new stochastic operational matrix (SOM) for the CWs… read more here.

Keywords: stochastic volterra; nonlinear stochastic; method; volterra integral ... See more keywords
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Numerical Solutions of Stochastic Volterra–Fredholm Integral Equations by Hybrid Legendre Block-Pulse Functions

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recommendations! Published in 2018 at "International Journal of Nonlinear Sciences and Numerical Simulation"

DOI: 10.1515/ijnsns-2017-0038

Abstract: Abstract In this article, the numerical solutions of stochastic Volterra–Fredholm integral equations have been obtained by hybrid Legendre block-pulse functions (BPFs) and stochastic operational matrix. The hybrid Legendre BPFs are orthonormal and have compact support… read more here.

Keywords: stochastic volterra; hybrid legendre; solutions stochastic; numerical solutions ... See more keywords
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Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels

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recommendations! Published in 2019 at "Bernoulli"

DOI: 10.3150/20-bej1284

Abstract: We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance.… read more here.

Keywords: equations kernels; volterra; volterra equations; existence uniqueness ... See more keywords