Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients

Bao, Jianhai; Huang, Xing

doi:10.1007/s10959-021-01082-9

Cited by 33 publications

(13 citation statements)

References 23 publications

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“…where s δ := ⌊s/δ⌋δ. This, together with the Hölder inequality and Itô isometry, further implies that E|Φ i,N, (1) n,ε…”

Section: Lemma 34 Let (A1) and (A2) Hold Then For Any Initial Valuementioning

confidence: 82%

“…Proof. We will prove this result by iterating in distribution which is similar to the argument of [1]. For each k ≥ 1, consider the following distribution-iterated SDEs…”

Section: Lemma 31 Assume That (A1) and (A2) Hold For Any Initial Valuementioning

confidence: 91%

“…Substituting these inequalities into (3.24), by the Hölder inequality and using (3.23) lead to E|Φ i,N, (1) n,ε…”

Section: Lemma 34 Let (A1) and (A2) Hold Then For Any Initial Valuementioning

confidence: 99%

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Least squares estimation for distribution-dependent stochastic differential delay equations

Zhu

2022

CPAA

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<p style='text-indent:20px;'>The parametric estimation of drift parameter for distribution - dependent stochastic differential delay equations with a small diffusion is presented. The principle technique of our investigation is to construct an appropriate contrast function and carry out a limiting type of argument to show the consistency and convergence rate of the least squares estimator of the drift parameter via interacting particle systems. In addition, two examples are constructed to demonstrate the effectiveness of our work.</p>

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“…where s δ := ⌊s/δ⌋δ. This, together with the Hölder inequality and Itô isometry, further implies that E|Φ i,N, (1) n,ε…”

Section: Lemma 34 Let (A1) and (A2) Hold Then For Any Initial Valuementioning

confidence: 82%

“…Proof. We will prove this result by iterating in distribution which is similar to the argument of [1]. For each k ≥ 1, consider the following distribution-iterated SDEs…”

Section: Lemma 31 Assume That (A1) and (A2) Hold For Any Initial Valuementioning

confidence: 91%

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Least squares estimation for distribution-dependent stochastic differential delay equations

Zhu

2022

CPAA

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“…Recently, [19] has proved Wang's Harnack inequality and super Poincaré inequality for (1.1). [6] investigated the strong well-posedness and propagation chaos of McKean-Vlasov SDEs with Hölder continuous diffusion coefficients, and the diffusion is assumed to be distribution free. When the diffusion depends on distribution, the Yamada-Watanabe approximation is unavailable, and the strong well-posedness is still open.…”

Section: Introductionmentioning

confidence: 99%

Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent CKLS and Vasicek Model

Bai

Huang

2021

Preprint

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In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order θ with θ ∈ [ 1 2 , 1); the other one is Vasicek model, where the diffusion coefficient only depends on distribution. Both models in the distribution independent case are used to characterize the interest rate in finance.

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“…Compared with the approximation of NSDDEs, the numerical method for MV-NSDDEs needs to approximate the law at each grid. Recently, a few works paid attention to the numerical methods for MV-SDEs (see, e.g., [1,2,4,5,6]). Especially, using the tamed EM scheme and the theory of propagation of chaos, Dos-Reis et al [3,10] gave the strong convergence of the numerical solutions for MV-SDEs, [24] studied least squares estimator for a class of path-dependent MV-SDEs by adopting a tamed Euler-Maruyama algorithm.…”

Section: Introductionmentioning

confidence: 99%

Explicit Numerical Approximations for McKean-Vlasov Neutral Stochastic Differential Delay Equations

Liu

Chen

2021

Preprint

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This paper studies the convergence of the tamed Euler-Maruyama (EM) scheme for a class of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the drift coefficients satisfy the super-linear growth condition. We provide the existence and uniqueness of strong solutions to MV-NSDDEs. Then, we use a stochastic particle method, which is based upon the theory of the propagation of chaos between particle system and the original MV-NSDDE, to deal with the approximation of the law. Moreover, we obtain the convergence rate of tamed EM scheme with respect to the corresponding particle system. Combining the result of propagation of chaos and the convergence rate of the numerical solution to the particle system, we get a convergence error between the numerical solution and exact solution of the original MV-NSDDE in the stepsize and number of particles.

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Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients

Cited by 33 publications

References 23 publications

Least squares estimation for distribution-dependent stochastic differential delay equations

Least squares estimation for distribution-dependent stochastic differential delay equations

Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent CKLS and Vasicek Model

Explicit Numerical Approximations for McKean-Vlasov Neutral Stochastic Differential Delay Equations

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